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1 Swap Derivatives: Forward Swaps and Swaptions
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  • *

    Swap Derivatives: Forward Swaps and Swaptions

  • *Swap DerivativesToday, there are a number of nonstandard or non-generic swaps used by financial and non-financial corporations to manage their varied cash flow and asset and liability positions.

    Two of the most widely used non-generic swaps are the forward swap and options on swaps or swaptions.

    A forward swap is an agreement to enter into a swap that starts at a future date at an interest rate agreed upon today.

    A swaption, in turn, is a right, but not an obligation, to take a position on a swap at a specific swap rate.

  • *Forward SwapsLike futures and farward contracts on debt securities, forward swaps provide borrowers and investors with a tool for locking in a future interest rate.

    As such, they can be used to manage interest rate risk for fixed-income positions.

  • *Hedging a Future Loan with a Forward SwapFinancial and non-financial institutions that have future borrowing obligations can lock in a future rate by obtaining forward contracts on fixed-payer swap positions.

  • *Hedging a Future LoanExample: A company wishing to lock in a rate on a 5-year, fixed-rate $100,000,000 loan to start two years from today, could enter a 2-year forward swap agreement to pay the fixed rate on a five-year 9%/LIBOR swap.

    At the expiration date on the forward swap, the company could issue $100,000,000 floating-rate debt at LIBOR that, when combined with the fixed position on the swap, would provide the company with a synthetic fixed rate loan paying 9% on the floating debt.

  • *Hedging a Future Loan

    InstrumentActionIssue Flexible Rate NoteSwap: Fixed-Rate Payers PositionSwap: Fixed-Rate Payers Position Pay LIBORPay Fixed RateReceive LIBOR LIBOR9%+LIBOR Synthetic Fixed Rate Net Payment 9%

  • *Hedging a Future LoanAlternatively, at the forward swaps expiration date, the company could sell the 5-year 9%/LIBOR swap underlying the forward swap contract and issue a 5-year fixed-rate bond.

    If the rate on 5-year fixed rate bond were higher than 9%, for example at 10%, then the company would be able offset the higher interest by selling its fixed position on the 9%/LIBOR swap to a swap dealer for an amount equal to the present value of a 5-year annuity equal to 1% (difference in rates: 10% 9%) times the NP.

  • *Hedging a Future LoanFor example, at 10% the value of the underlying 9%/LIBOR swap would be $3.8609 million using the YTM swap valuation approach:

  • *Hedging a Future LoanWith the proceeds of $3.8609 million from closing its swap, the company would only need to raise $96.1391 million (= $100 million $3.8609 million).

    The company, though, would have to issue $96.1391 million worth of 5-year fixed-rate bonds at the higher 10% rate.

    This would result in semiannual interest payments of $4.8070 million (= (.10/2)($96.1391 million), and the total return based on the $100 million funds needed would be approximately 9%.

  • *Hedging a Future LoanIf the rate on 5-year fixed rate loans were lower than 9%, say 8%, then the company would benefit from the lower fixed rate loan, but would lose an amount equal to the present value of a 5-year annuity equal to 1% (difference in rates: 8% 9%) times the NP when it closed the fixed position.

    Specifically, at 8%, the value of the underlying 9%/LIBOR swap is $4.055 million using the YTM approach:

  • *Hedging a Future LoanThe company would therefore have to pay the swap bank $4.055 million for assuming its fixed-payers position.

    With a payment of $4.055 million, the company would need to raise a total of $104.055 million from its bond issue.

    The company, though, would be able to issue $104.055 million worth of 5-year fixed-rate bonds at the lower rate of 8% rate.

    Its semiannual interest payments would be $4.1622 million (= .08/2)($104.055 million), and its total return based on the $100 million funds needed would be approximately 9%.

  • *Hedging a Future InvestmentForward swaps can also be used on the asset side to fix the rate on a future investment.

    Consider the case of an institutional investor planning to invest an expected $10 million cash inflow one year from now in a 3-year, high quality fixed-rate bond.

    The investor could lock in the future rate by entering a 1-year forward swap agreement to receive the fixed rate and pay the floating rate on a 3-year, 9%/LIBOR swap with a NP of $10 million.

  • *Hedging a Future InvestmentAt the expiration date on the forward swap, the investor could invest the $10 million cash inflow in a 3-year FRN at LIBOR that, which when combined with the floating position on the swap, would provide the investor with a synthetic fixed rate-loan paying 9%.

  • *Hedging a Future Investment

    InstrumentActionBuy Flexible Rate NoteSwap: Floating-Rate Payers PositionSwap: Floating-Rate Payers Position Receive LIBORPay LIBORReceive Fixed Rate LIBORLIBOR+9% Synthetic Fixed Rate InvestmentNet Receipt 9%

  • *Hedging a Future InvestmentInstead of forming a synthetic fixed investment position, the investor alternatively could sell the 3-year 9%/LIBOR swap underlying the forward swap contract and invest in a 3-year fixed-rate note.

    If the rate on the 3-year fixed rate note were lower than the 9% swap rate, then the investor would be able to sell his floating position at a value equal to the present value of an annuity equal to the $10 million NP times the difference between 9% and the rate on 3-year fixed rate bonds; this gain would offset the lower return on the fixed-rate bond.

  • *Hedging a Future InvestmentExample: If at the forward swaps expiration date, the rate on 3-year, fixed rate bonds were at 8%, and the fixed rate on a 3-year par value swap were at 8%, then the investment firm would be able to sell its floating-payers position on the 3-year 9%/LIBOR swap underlying the forward swap contract to a swap bank for $262,107 (using the YTM approach with a discount rate of 8%):

  • *Hedging a Future InvestmentThe investment firm would therefore invest $10 million plus the $262,107 proceeds from closing its swap position.

    The total return based on an investment of $10 million, though, would be approximately equal to 9%.

  • *Hedging a Future InvestmentOn the other hand, if the rate on 3-year fixed-rate securities were higher than 9%, the investment company would benefit from the higher investment rate, but would lose on closing its swap position.

    Example: If at the forward swaps expiration date, the rate on 3-year, fixed rate bonds were at 10% and the fixed rate on a 3-year par value swap were at 10%, then the investment firm would have to pay the swap bank $253,785 for assuming its floating-payers position on the 3-year 9%/LIBOR swap underlying the forward swap contract:

  • *Hedging a Future InvestmentThe investment firm would therefore invest $9,746,215 ($10,000,000 minus the $253,785 costs incurred in closing its swap) in 3-year, fixed rate bonds yielding 10%.

    The total return based on an investment of $10 million funds, though, would be approximately equal to 9%.

  • *Other Uses of Forward SwapsThe examples illustrate that forward swaps are like futures on debt securities.

    As such, they are used in many of the same ways as futures: Locking in future interest ratesSpeculating on future interest rate changesAltering a balance sheets exposure to interest rate changes

    Different from futures, though, forward swaps can be customized to fit a particular investment or borrowing need and with the starting dates on forward swaps ranging anywhere from one month to several years, they can be applied to not only short-run but also long-run positions.

  • *SwaptionsOne of the most innovative non-generic swaps is the swap option or simply swaption.

    As the name suggests, a swaption is an option on a swap.

    The purchaser of a swaption buys the right to start an interest rate swap with a specific fixed rate or exercise rate, and with a maturity at or during a specific time period in the future.

    If the holder exercises, she takes the swap position, with the swap seller obligated to take the opposite counterparty position.

    For swaptions, the underlying instrument is a forward swap and the option premium is the up-front fee.

  • *SwaptionsThe swaption can be either a receiver swaption or a payer swaption:

    A receiver swaption gives the holder the right to receive a specific fixed rate and pay the floating rate The right to take a floating payers position

    A payer swaption gives the holder the right to pay a specific fixed rate and receive the floating rate The right to take a fixed payers position

  • *SwaptionsSwaptions can be either European or American: A European swaption can be exercised only at a specific point in time, usually just before the starting date on the swap.

    An American swaption is exercisable at any point in time during a specified period of time.

  • *SwaptionsSwaptions are similar to interest rate options or options on debt securities. They are, however, more varied:

    They can range from options to begin a 1-year swap in 3 months to a 10-year option on a 8-year swap (sometimes referred to as a 10 x 8 swaption).

    The exercise periods can vary for American swaptions.

    Swaptions can be written on generic swaps or non-generic swaps.

  • *SwaptionsLike interest rate and debt options, swaptions can be used for:Speculating on interest rates

    Hedging debt and asset positions against market risk

    Combined with other securities to create synthetic positions

  • *Swaptions: SpeculationSuppose a speculator expects the rate on high quality, 5-year fixed rate bonds to increase from their current 8% level.

    As an alternative to a short T-note futures position or an interest rate call, the speculator could buy a payer swaption.

  • *Swaptions: SpeculationSuppose the speculator elects to buy a 1-year European payer swaption on a 5-year, 8%/LIBOR swap with a NP of $10,000,00 for 50 bp times the NP:1 x 5 payer swaptionExercise date = 1 year Exercise rate = 8%Underlying swap = 5-year, 8%/LIBOR with NP = $10,000,000 Swap position = fixed payerOption premium = 50 bp times NP

  • *Swaptions: SpeculationOn the exercise date, if the fixed rate on a 5-year swap were greater than the exercise rate of 8%, then the speculator would exercise her right to pay the fixed rate below the market rate.

    To realize the gain, she could take her 8% fixed-rate payers swap position obtained from exercising and sell it to another counterparty.

  • *Swaptions: SpeculationFor example, if the 5-year par value swap were trading at 9% and swaps were valued by the YTM approach, then she would be able to sell her 8% swap for $395,636:

    If the swap rate at the expiration date were less than 8%, then the payer swaption would have no value and the speculator would simple let it expire, losing the premium she paid.

  • *Swaptions: SpeculationFormally, the value of the payer swaption at expiration is:

    For rates, R, on par value 5-year swaps exceeding the exercise rate of 8%, the value of the payer swaption will be equal to the present value of the interest differential times the notional principal on the swap.

    For rates less than or equal to 8%, the swap is worthless.

    The next slide shows graphically and in a table the values and profits at expiration obtained from closing the payer swaption on the 5-year 8%/LIBOR swap given different rates at expiration.

  • *Value and Profit at Expiration from 8%/LIBOR Payer Swaption

    5.2-1

    123456

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedNet Interest Received

    Payer's Payment*Payer's Payment**by Fixed-Rate Payerby Floating-Rate Payer

    Column 3 - Column 4Column 4 - Column 3

    3/1/030.045

    9/1/030.05225000275000-5000050000

    3/1/040.055250000275000-2500025000

    9/1/040.0627500027500000

    3/1/050.06530000027500025000-25000

    9/1/050.0732500027500050000-50000

    3/1/0635000027500075000.0000000001-75000.0000000001

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    5.2-2

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Fixed-Rate PayerFloating-Rate Loan*and LoanAnnualized Rate***

    Column 3 - Column 4Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000-500002250002750000.055

    3/1/040.055250000275000-250002500002750000.055

    9/1/040.0627500027500002750002750000.055

    3/1/050.065300000275000250003000002750000.055

    9/1/050.07325000275000500003250002750000.055

    3/1/0635000027500075000.00000000013500002750000.055

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-3

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Floating-Rate Payer5% Fixed-Rate Loanand LoanAnnualized Rate***

    Column 4 - Column 3Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000500002500002000000.04

    3/1/040.055250000275000250002500002250000.045

    9/1/040.0627500027500002500002500000.05

    3/1/050.065300000275000-250002500002750000.055

    9/1/050.07325000275000-500002500003000000.06

    3/1/06350000275000-75000.00000000012500003250000.065

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-4

    1234

    Closing DatesLIBORfTCash Flow*

    10[f0 - fT]

    9/1/035975000-25000

    3/1/045.59725000

    9/1/04697000025000

    3/1/056.596750050000

    9/1/05796500075000

    f0 = 972,500

    15.3-2

    Swap MaturityTreasury YieldBid Swap Spread (BP)Ask Swap Spread (BP)Fixed Swap Rate SpreadSwap Rate

    2 year4.98%67745.65% - 5.72%5.69%

    3 year5.17%72765.89% - 5.93%5.91%

    4 year5.38%69746.07% - 6.12%6.10%

    5 year5.50%70766.20% - 6.26%6.23%

    15.3-3

    Fixed-Rate Payers Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net Payment

    6/10/025.50%

    12/10/021835.75%627715.068493151559166.66666666768548.4018264841

    6/10/031826.00%624284.931506849581388.88888888942896.0426179605

    12/10/031836.25%627715.06849315161000017715.0684931509

    6/10/041826.50%624284.931506849631944.444444444-7659.512937595

    12/10/041836.75%627715.068493151660833.333333333-33118.2648401825

    6/10/04182624284.931506849682500-58215.0684931506

    Fixed Payment = (.0626)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    15.4-1

    123456

    Maturity in YearsYield on T-NoteSwap Spread (BP)Swap RateZero Coupon RateImplied 1-year Forward Rates5 year4 year3 year2 YEAR1 YEAR

    10.041000.050.050.05600857144.76190476194.76190476190.04761904764.7619047619100

    20.045800.0530.053080.06504564185.05046965475.05046965470.050504696595.2236257615

    30.05700.0570.057290.07511527465.5034601885.5034601880.055034601999.9855305234

    40.055650.06150.0621760.08520902525.901227016484.46350414230.153158346

    50.06620.06620.067469778.295285946799.779338747

    99.5123475678

    Year5-YEAR

    10.050.0066666667

    20.053080.0063121209

    30.057290.0059226445

    40.0621760.059012054578.5622771259189014.321050802

    50.06746970.06147629572.1476546259

    0.1204883495150.70993175180.0007994719

    15.5-1

    Swap: Fixed payer's position on 8%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%802191.78082191876250039691.7808219179864166.666666667903858.4474885840.0901388889

    6/10/031828.00%797808.219178082783611.11111111114197.1080669712884722.222222222898919.3302891930.0901388889

    12/10/031838.25%802191.780821918813333.333333333-11141.5525114153915000903858.4474885850.0901388889

    6/10/041828.50%797808.219178082834166.666666667-36358.4474885844935277.777777778898919.3302891930.0901388889

    12/10/041838.75%802191.780821918864166.666666667-61974.8858447488965833.333333333903858.4474885840.0901388889

    6/10/051829.00%797808.219178082884722.222222222-86914.0030441399985833.333333333898919.3302891930.0901388889

    12/10/051839.25%802191.780821918915000-112808.2191780821016666.66666667903858.4474885840.0901388889

    6/10/061829.50%797808.219178082935277.777777778-137469.5585996961036388.88888889898919.3302891930.0901388889

    12/10/061839.75%802191.780821918965833.333333333-163641.5525114151067500903858.4474885840.0901388889

    6/10/0718210.00%797808.219178082985833.333333333-188025.1141552511086944.44444444898919.3302891930.0901388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    15.5-2

    Swap: Floating payer's position on 9.5%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%952602.739726028762500-190102.739726028902465.753424658712363.013698630.0700684932

    6/10/031828.00%947397.260273973783611.111111111-163786.149162862897534.246575342733748.0974124810.0725684932

    12/10/031838.25%952602.739726028813333.333333333-139269.406392694902465.753424658763196.3470319630.0750684932

    6/10/041828.50%947397.260273973834166.666666667-113230.593607306897534.246575342784303.6529680360.0775684932

    12/10/041838.75%952602.739726028864166.666666667-88436.0730593608902465.753424658814029.6803652970.0800684932

    6/10/051829.00%947397.260273973884722.222222222-62675.0380517505897534.246575342834859.2085235920.0825684932

    12/10/051839.25%952602.739726028915000-37602.7397260276902465.753424658864863.013698630.0850684932

    6/10/061829.50%947397.260273973935277.777777778-12119.4824961949897534.246575342885414.7640791480.0875684932

    12/10/061839.75%952602.739726028965833.33333333313230.5936073057902465.753424658915696.3470319630.0900684932

    6/10/0718210.00%947397.260273973985833.33333333338436.0730593606897534.246575342935970.3196347030.0925684932

    Fixed Payment = (.095)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    15.5-3

    Swap: Floating payer's position on 5.75%/LIBOR Swap; NP = $1000M; Maturity = 5 years.

    Investment in $1000M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%2882876.712328772287500-595376.7123287682795833.333333333391210.04566210.0676388889

    6/10/031825.00%2867123.287671232401388.88888889-465734.3987823452906944.444444443372678.843226790.0676388889

    12/10/031835.25%2882876.712328772541666.66666667-341210.04566210130500003391210.04566210.0676388889

    6/10/041825.50%2867123.287671232654166.66666667-212956.6210045673159722.222222223372678.843226790.0676388889

    12/10/041835.75%2882876.712328772795833.33333333-87043.37899543483304166.666666673391210.04566210.0676388889

    6/10/051826.00%2867123.287671232906944.4444444439821.156773211434125003372678.843226790.0676388889

    12/10/051836.25%2882876.712328773050000167123.2876712323558333.333333333391210.04566210.0676388889

    6/10/061826.50%2867123.287671233159722.22222222292598.9345509893665277.777777783372678.843226790.0676388889

    12/10/061836.75%2882876.712328773304166.66666667421289.95433789938125003391210.04566210.0676388889

    6/10/071827.00%2867123.287671233412500545376.7123287673918055.555555563372678.843226790.0676388889

    Fixed Payment = (.0575)(no. of days/365)($100,000,000)

    Floating Payment = LIBOR(no. of days/360)($100,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($100,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$100,000,000

    syn fixed swap

    Swap: Fixed payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500139965.753424658864166.6666666671004132.420091320.1001388889

    6/10/031828.00%897534.246575342783611.111111111113923.135464231884722.222222222998645.3576864540.1001388889

    12/10/031838.25%902465.753424658813333.33333333389132.42009132449150001004132.420091320.1001388889

    6/10/041828.50%897534.246575342834166.66666666763367.5799086759935277.777777778998645.3576864540.1001388889

    12/10/041838.75%902465.753424658864166.66666666738299.0867579909965833.3333333331004132.420091320.1001388889

    6/10/051829.00%897534.246575342884722.22222222212812.0243531204985833.333333333998645.3576864530.1001388889

    12/10/051839.25%902465.753424658915000-12534.24657534241016666.666666671004132.420091320.1001388889

    6/10/061829.50%897534.246575342935277.777777778-37743.53120243531036388.88888889998645.3576864530.1001388889

    12/10/061839.75%902465.753424658965833.333333333-63367.579908675610675001004132.420091320.1001388889

    6/10/0718210.00%897534.246575342985833.333333333-88299.08675799081086944.44444444998645.3576864540.1001388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    syn var

    Swap: Floating payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500-139965.753424658902465.7534246587625000.075

    6/10/031828.00%897534.246575342783611.111111111-113923.135464231897534.246575342783611.1111111110.0775

    12/10/031838.25%902465.753424658813333.333333333-89132.4200913244902465.753424658813333.3333333330.08

    6/10/041828.50%897534.246575342834166.666666667-63367.5799086759897534.246575342834166.6666666670.0825

    12/10/041838.75%902465.753424658864166.666666667-38299.0867579909902465.753424658864166.6666666670.085

    6/10/051829.00%897534.246575342884722.222222222-12812.0243531204897534.246575342884722.2222222220.0875

    12/10/051839.25%902465.75342465891500012534.2465753424902465.7534246589150000.09

    6/10/061829.50%897534.246575342935277.77777777837743.5312024353897534.246575342935277.7777777780.0925

    12/10/061839.75%902465.753424658965833.33333333363367.5799086756902465.753424658965833.3333333330.095

    6/10/0718210.00%897534.246575342985833.33333333388299.0867579908897534.246575342985833.3333333330.0975

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    Synfixinv

    Swap: Floating payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment in $20M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500-144143.835616438559166.666666667703310.5022831050.0701388889

    6/10/031825.00%598356.164383562480277.777777778-118078.386605784581388.888888889699467.2754946730.0701388889

    12/10/031835.25%601643.835616438508333.333333333-93310.502283105610000703310.5022831050.0701388889

    6/10/041825.50%598356.164383562530833.333333333-67522.8310502284631944.444444444699467.2754946730.0701388889

    12/10/041835.75%601643.835616438559166.666666667-42477.1689497718660833.333333333703310.5022831050.0701388889

    6/10/051826.00%598356.164383562581388.888888889-16967.2754946728682500699467.2754946730.0701388889

    12/10/051836.25%601643.8356164386100008356.1643835615711666.666666667703310.5022831050.0701388889

    6/10/061826.50%598356.164383562631944.44444444433588.2800608827733055.555555556699467.2754946730.0701388889

    12/10/061836.75%601643.835616438660833.33333333359189.4977168948762500703310.5022831050.0701388889

    6/10/071827.00%598356.16438356268250084143.8356164383783611.111111111699467.2754946730.0701388889

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$20,000,000

    synflinvoat

    Swap: Fixed payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment of $20M in 5-year bond 7%. Synthetic fixed-rate investment: Fixed Investment and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Payer's Net PaymentFixed Investment ReturnFixed Inv Return - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500144143.835616438701917.808219178557773.972602740.055625

    6/10/031825.00%598356.164383562480277.777777778118078.386605784698082.191780822580003.8051750380.0581597222

    12/10/031835.25%601643.835616438508333.33333333393310.502283105701917.808219178608607.3059360730.0606944444

    6/10/041825.50%598356.164383562530833.33333333367522.8310502284698082.191780822630559.3607305930.0632291667

    12/10/041835.75%601643.835616438559166.66666666742477.1689497718701917.808219178659440.6392694060.0657638889

    6/10/051826.00%598356.164383562581388.88888888916967.2754946728698082.191780822681114.9162861490.0682986111

    12/10/051836.25%601643.835616438610000-8356.1643835615701917.808219178710273.972602740.0708333333

    6/10/061826.50%598356.164383562631944.444444444-33588.2800608827698082.191780822731670.4718417050.0733680556

    12/10/061836.75%601643.835616438660833.333333333-59189.4977168948701917.808219178761107.3059360730.0759027778

    6/10/071827.00%598356.164383562682500-84143.8356164383698082.191780822782226.027397260.0784375

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Investment Return = 7%(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Inv Return - Swap Payment)(365/no. of days)/$20,000,000

    Put-call Parity

    Values at Expiration of Put Swaption and Synthetic Put Swaption consisting of Call Swaption and Forward Contract

    Swap Rates on 2-Year Generic Swap6%7%8%

    Long Put Swaption: Right to pay 7%/receive LIBOR00PV(8%-7%)

    Long Call Swaption: Right to Receive 7%/pay LIBORPV(7%-6%)00

    Swap from Forward: Pay 7%/Receive LIBORPV(6%-7%)PV(7%-7%)PV(8%-7%)

    Net Value00PV(8%-7%)

    PV = present value of two-year cash flows

    Exhibit17.4-1

    Rates on 5-year Par ValuePayer Swaption'sValue of 8%/LIBORPayer SwaptionProfit from Payer

    Swaps at ExpirationInterest DifferentialPayer Swaption at ExpiationCostSwaption

    RMax((R.08)/2,0)PV(Max[(R.08)/2, 0]($10m))

    0.0600.0000$0$50,000-$50,000

    0.0650.0000$0$50,000-$50,000

    0.0700.0000$0$50,000-$50,000

    0.0750.0000$0$50,000-$50,000

    0.0800.0000$0$50,000-$50,000

    0.0850.0025$200,272$50,000$150,272

    0.0900.0050$395,636$50,000$345,636

    0.0950.0075$586,226$50,000$536,226

    0.1000.0100$772,173$50,000$722,173

    Exhibit17.4-1

    Rates

    Profit

    eXHIBIT17.4-2

    Rates on 5-year Par ValueCall Swaption'sValue of 8%/LIBORCall SwaptionProfit from Call

    Swaps at ExpirationInterest DifferentialCall Swaption at ExpiationCostSwaption

    RMax((.08-R)/2,0)PV(Max[(.08-R)/2, 0]($50M))

    0.0600.01085302050000803020

    0.0650.00863168050000581680

    0.0700.00541583050000365830

    0.0750.00320532050000155320

    0.0800.000050000-50000

    0.0850.000050000-50000

    0.0900.000050000-50000

    0.0950.000050000-50000

    0.1000.000050000-50000

    eXHIBIT17.4-2

    Rates

    Profit

    16.6-5

    123456

    Year$ CF (millions) CF (millions)Forward Exchange: /BP$ Cost of Sterling (millions)Net $ Revenue (millions)

    Column (4) X Column (3)Column (2) - Column (5)

    10.60.7140.7163550.511477470.08852253

    20.60.7140.733090.523426260.07657374

    30.60.7140.750220.535657080.06434292

    40.60.7140.767750.54817350.0518265

    50.60.7140.7856870.5609805180.039019482

    0.320285172

    16.6-2

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    NOTE THAT THESE CHANGES ARE LIKELY TO CHANGE TOGETHER

    16.6-3

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    ch17prob31

    123456

    Year$ CF (millions) CF (millions)Forward Exchange: /BP$ Cost of Sterling (millions)Net $ Revenue (millions)

    Column (4) X Column (3)Column (2) - Column (5)

    10.857142-0.51.46194780.73097390.12617

    20.857142-0.51.49610550.748052750.10909

    30.857142-0.51.53106120.76553060.09161

    40.857142-0.51.56683360.78341680.07373

    50.857142-0.51.60344190.801720950.05542

    0.45602

    MBD000B2C9E.unknown

    Chart1

    -50000

    -50000

    -50000

    -50000

    -50000

    150272.175105954

    345635.908855507

    536226.075035174

    722173.492918481

    Rates

    Profit

    5.2-1

    123456

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedNet Interest Received

    Payer's Payment*Payer's Payment**by Fixed-Rate Payerby Floating-Rate Payer

    Column 3 - Column 4Column 4 - Column 3

    3/1/030.045

    9/1/030.05225000275000-5000050000

    3/1/040.055250000275000-2500025000

    9/1/040.0627500027500000

    3/1/050.06530000027500025000-25000

    9/1/050.0732500027500050000-50000

    3/1/0635000027500075000.0000000001-75000.0000000001

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    5.2-2

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Fixed-Rate PayerFloating-Rate Loan*and LoanAnnualized Rate***

    Column 3 - Column 4Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000-500002250002750000.055

    3/1/040.055250000275000-250002500002750000.055

    9/1/040.0627500027500002750002750000.055

    3/1/050.065300000275000250003000002750000.055

    9/1/050.07325000275000500003250002750000.055

    3/1/0635000027500075000.00000000013500002750000.055

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-3

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Floating-Rate Payer5% Fixed-Rate Loanand LoanAnnualized Rate***

    Column 4 - Column 3Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000500002500002000000.04

    3/1/040.055250000275000250002500002250000.045

    9/1/040.0627500027500002500002500000.05

    3/1/050.065300000275000-250002500002750000.055

    9/1/050.07325000275000-500002500003000000.06

    3/1/06350000275000-75000.00000000012500003250000.065

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-4

    1234

    Closing DatesLIBORfTCash Flow*

    10[f0 - fT]

    9/1/035975000-25000

    3/1/045.59725000

    9/1/04697000025000

    3/1/056.596750050000

    9/1/05796500075000

    f0 = 972,500

    15.3-2

    Swap MaturityTreasury YieldBid Swap Spread (BP)Ask Swap Spread (BP)Fixed Swap Rate SpreadSwap Rate

    2 year4.98%67745.65% - 5.72%5.69%

    3 year5.17%72765.89% - 5.93%5.91%

    4 year5.38%69746.07% - 6.12%6.10%

    5 year5.50%70766.20% - 6.26%6.23%

    15.3-3

    Fixed-Rate Payers Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net Payment

    6/10/025.50%

    12/10/021835.75%627715.068493151559166.66666666768548.4018264841

    6/10/031826.00%624284.931506849581388.88888888942896.0426179605

    12/10/031836.25%627715.06849315161000017715.0684931509

    6/10/041826.50%624284.931506849631944.444444444-7659.512937595

    12/10/041836.75%627715.068493151660833.333333333-33118.2648401825

    6/10/04182624284.931506849682500-58215.0684931506

    Fixed Payment = (.0626)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    15.4-1

    123456

    Maturity in YearsYield on T-NoteSwap Spread (BP)Swap RateZero Coupon RateImplied 1-year Forward Rates5 year4 year3 year2 YEAR1 YEAR

    10.041000.050.050.05600857144.76190476194.76190476190.04761904764.7619047619100

    20.045800.0530.053080.06504564185.05046965475.05046965470.050504696595.2236257615

    30.05700.0570.057290.07511527465.5034601885.5034601880.055034601999.9855305234

    40.055650.06150.0621760.08520902525.901227016484.46350414230.153158346

    50.06620.06620.067469778.295285946799.779338747

    99.5123475678

    Year5-YEAR

    10.050.0066666667

    20.053080.0063121209

    30.057290.0059226445

    40.0621760.059012054578.5622771259189014.321050802

    50.06746970.06147629572.1476546259

    0.1204883495150.70993175180.0007994719

    15.5-1

    Swap: Fixed payer's position on 8%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%802191.78082191876250039691.7808219179864166.666666667903858.4474885840.0901388889

    6/10/031828.00%797808.219178082783611.11111111114197.1080669712884722.222222222898919.3302891930.0901388889

    12/10/031838.25%802191.780821918813333.333333333-11141.5525114153915000903858.4474885850.0901388889

    6/10/041828.50%797808.219178082834166.666666667-36358.4474885844935277.777777778898919.3302891930.0901388889

    12/10/041838.75%802191.780821918864166.666666667-61974.8858447488965833.333333333903858.4474885840.0901388889

    6/10/051829.00%797808.219178082884722.222222222-86914.0030441399985833.333333333898919.3302891930.0901388889

    12/10/051839.25%802191.780821918915000-112808.2191780821016666.66666667903858.4474885840.0901388889

    6/10/061829.50%797808.219178082935277.777777778-137469.5585996961036388.88888889898919.3302891930.0901388889

    12/10/061839.75%802191.780821918965833.333333333-163641.5525114151067500903858.4474885840.0901388889

    6/10/0718210.00%797808.219178082985833.333333333-188025.1141552511086944.44444444898919.3302891930.0901388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    15.5-2

    Swap: Floating payer's position on 9.5%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%952602.739726028762500-190102.739726028902465.753424658712363.013698630.0700684932

    6/10/031828.00%947397.260273973783611.111111111-163786.149162862897534.246575342733748.0974124810.0725684932

    12/10/031838.25%952602.739726028813333.333333333-139269.406392694902465.753424658763196.3470319630.0750684932

    6/10/041828.50%947397.260273973834166.666666667-113230.593607306897534.246575342784303.6529680360.0775684932

    12/10/041838.75%952602.739726028864166.666666667-88436.0730593608902465.753424658814029.6803652970.0800684932

    6/10/051829.00%947397.260273973884722.222222222-62675.0380517505897534.246575342834859.2085235920.0825684932

    12/10/051839.25%952602.739726028915000-37602.7397260276902465.753424658864863.013698630.0850684932

    6/10/061829.50%947397.260273973935277.777777778-12119.4824961949897534.246575342885414.7640791480.0875684932

    12/10/061839.75%952602.739726028965833.33333333313230.5936073057902465.753424658915696.3470319630.0900684932

    6/10/0718210.00%947397.260273973985833.33333333338436.0730593606897534.246575342935970.3196347030.0925684932

    Fixed Payment = (.095)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    15.5-3

    Swap: Floating payer's position on 5.75%/LIBOR Swap; NP = $1000M; Maturity = 5 years.

    Investment in $1000M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%2882876.712328772287500-595376.7123287682795833.333333333391210.04566210.0676388889

    6/10/031825.00%2867123.287671232401388.88888889-465734.3987823452906944.444444443372678.843226790.0676388889

    12/10/031835.25%2882876.712328772541666.66666667-341210.04566210130500003391210.04566210.0676388889

    6/10/041825.50%2867123.287671232654166.66666667-212956.6210045673159722.222222223372678.843226790.0676388889

    12/10/041835.75%2882876.712328772795833.33333333-87043.37899543483304166.666666673391210.04566210.0676388889

    6/10/051826.00%2867123.287671232906944.4444444439821.156773211434125003372678.843226790.0676388889

    12/10/051836.25%2882876.712328773050000167123.2876712323558333.333333333391210.04566210.0676388889

    6/10/061826.50%2867123.287671233159722.22222222292598.9345509893665277.777777783372678.843226790.0676388889

    12/10/061836.75%2882876.712328773304166.66666667421289.95433789938125003391210.04566210.0676388889

    6/10/071827.00%2867123.287671233412500545376.7123287673918055.555555563372678.843226790.0676388889

    Fixed Payment = (.0575)(no. of days/365)($100,000,000)

    Floating Payment = LIBOR(no. of days/360)($100,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($100,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$100,000,000

    syn fixed swap

    Swap: Fixed payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500139965.753424658864166.6666666671004132.420091320.1001388889

    6/10/031828.00%897534.246575342783611.111111111113923.135464231884722.222222222998645.3576864540.1001388889

    12/10/031838.25%902465.753424658813333.33333333389132.42009132449150001004132.420091320.1001388889

    6/10/041828.50%897534.246575342834166.66666666763367.5799086759935277.777777778998645.3576864540.1001388889

    12/10/041838.75%902465.753424658864166.66666666738299.0867579909965833.3333333331004132.420091320.1001388889

    6/10/051829.00%897534.246575342884722.22222222212812.0243531204985833.333333333998645.3576864530.1001388889

    12/10/051839.25%902465.753424658915000-12534.24657534241016666.666666671004132.420091320.1001388889

    6/10/061829.50%897534.246575342935277.777777778-37743.53120243531036388.88888889998645.3576864530.1001388889

    12/10/061839.75%902465.753424658965833.333333333-63367.579908675610675001004132.420091320.1001388889

    6/10/0718210.00%897534.246575342985833.333333333-88299.08675799081086944.44444444998645.3576864540.1001388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    syn var

    Swap: Floating payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500-139965.753424658902465.7534246587625000.075

    6/10/031828.00%897534.246575342783611.111111111-113923.135464231897534.246575342783611.1111111110.0775

    12/10/031838.25%902465.753424658813333.333333333-89132.4200913244902465.753424658813333.3333333330.08

    6/10/041828.50%897534.246575342834166.666666667-63367.5799086759897534.246575342834166.6666666670.0825

    12/10/041838.75%902465.753424658864166.666666667-38299.0867579909902465.753424658864166.6666666670.085

    6/10/051829.00%897534.246575342884722.222222222-12812.0243531204897534.246575342884722.2222222220.0875

    12/10/051839.25%902465.75342465891500012534.2465753424902465.7534246589150000.09

    6/10/061829.50%897534.246575342935277.77777777837743.5312024353897534.246575342935277.7777777780.0925

    12/10/061839.75%902465.753424658965833.33333333363367.5799086756902465.753424658965833.3333333330.095

    6/10/0718210.00%897534.246575342985833.33333333388299.0867579908897534.246575342985833.3333333330.0975

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    Synfixinv

    Swap: Floating payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment in $20M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500-144143.835616438559166.666666667703310.5022831050.0701388889

    6/10/031825.00%598356.164383562480277.777777778-118078.386605784581388.888888889699467.2754946730.0701388889

    12/10/031835.25%601643.835616438508333.333333333-93310.502283105610000703310.5022831050.0701388889

    6/10/041825.50%598356.164383562530833.333333333-67522.8310502284631944.444444444699467.2754946730.0701388889

    12/10/041835.75%601643.835616438559166.666666667-42477.1689497718660833.333333333703310.5022831050.0701388889

    6/10/051826.00%598356.164383562581388.888888889-16967.2754946728682500699467.2754946730.0701388889

    12/10/051836.25%601643.8356164386100008356.1643835615711666.666666667703310.5022831050.0701388889

    6/10/061826.50%598356.164383562631944.44444444433588.2800608827733055.555555556699467.2754946730.0701388889

    12/10/061836.75%601643.835616438660833.33333333359189.4977168948762500703310.5022831050.0701388889

    6/10/071827.00%598356.16438356268250084143.8356164383783611.111111111699467.2754946730.0701388889

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$20,000,000

    synflinvoat

    Swap: Fixed payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment of $20M in 5-year bond 7%. Synthetic fixed-rate investment: Fixed Investment and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Payer's Net PaymentFixed Investment ReturnFixed Inv Return - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500144143.835616438701917.808219178557773.972602740.055625

    6/10/031825.00%598356.164383562480277.777777778118078.386605784698082.191780822580003.8051750380.0581597222

    12/10/031835.25%601643.835616438508333.33333333393310.502283105701917.808219178608607.3059360730.0606944444

    6/10/041825.50%598356.164383562530833.33333333367522.8310502284698082.191780822630559.3607305930.0632291667

    12/10/041835.75%601643.835616438559166.66666666742477.1689497718701917.808219178659440.6392694060.0657638889

    6/10/051826.00%598356.164383562581388.88888888916967.2754946728698082.191780822681114.9162861490.0682986111

    12/10/051836.25%601643.835616438610000-8356.1643835615701917.808219178710273.972602740.0708333333

    6/10/061826.50%598356.164383562631944.444444444-33588.2800608827698082.191780822731670.4718417050.0733680556

    12/10/061836.75%601643.835616438660833.333333333-59189.4977168948701917.808219178761107.3059360730.0759027778

    6/10/071827.00%598356.164383562682500-84143.8356164383698082.191780822782226.027397260.0784375

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Investment Return = 7%(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Inv Return - Swap Payment)(365/no. of days)/$20,000,000

    Put-call Parity

    Values at Expiration of Put Swaption and Synthetic Put Swaption consisting of Call Swaption and Forward Contract

    Swap Rates on 2-Year Generic Swap6%7%8%

    Long Put Swaption: Right to pay 7%/receive LIBOR00PV(8%-7%)

    Long Call Swaption: Right to Receive 7%/pay LIBORPV(7%-6%)00

    Swap from Forward: Pay 7%/Receive LIBORPV(6%-7%)PV(7%-7%)PV(8%-7%)

    Net Value00PV(8%-7%)

    PV = present value of two-year cash flows

    Exhibit17.4-1

    Rates on 5-year Par ValuePut Swaption'sValue of 8%/LIBORPut SwaptionProfit from Put

    Swaps at ExpirationInterest DifferentialPut Swaption at ExpiationCostSwaption

    RMax((R-.08)/2,0)PV(Max[(R-.08)/2, 0]($50M))

    0.0600.000050000-50000

    0.0650.000050000-50000

    0.0700.000050000-50000

    0.0750.000050000-50000

    0.0800.000050000-50000

    0.0850.00320027250000150272

    0.0900.00539563650000345636

    0.0950.00858622650000536226

    0.1000.01077217350000722173

    Exhibit17.4-1

    Rates

    Profit

    eXHIBIT17.4-2

    Rates on 5-year Par ValueCall Swaption'sValue of 8%/LIBORCall SwaptionProfit from Call

    Swaps at ExpirationInterest DifferentialCall Swaption at ExpiationCostSwaption

    RMax((.08-R)/2,0)PV(Max[(.08-R)/2, 0]($50M))

    0.0600.01085302050000803020

    0.0650.00863168050000581680

    0.0700.00541583050000365830

    0.0750.00320532050000155320

    0.0800.000050000-50000

    0.0850.000050000-50000

    0.0900.000050000-50000

    0.0950.000050000-50000

    0.1000.000050000-50000

    eXHIBIT17.4-2

    Rates

    Profit

    16.6-5

    123456

    Year$ CF (millions) CF (millions)Forward Exchange: /BP$ Cost of Sterling (millions)Net $ Revenue (millions)

    Column (4) X Column (3)Column (2) - Column (5)

    10.60.7140.7163550.511477470.08852253

    20.60.7140.733090.523426260.07657374

    30.60.7140.750220.535657080.06434292

    40.60.7140.767750.54817350.0518265

    50.60.7140.7856870.5609805180.039019482

    0.320285172

    16.6-2

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    NOTE THAT THESE CHANGES ARE LIKELY TO CHANGE TOGETHER

    16.6-3

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    MBD00009CED.unknown

  • *Swaptions: SpeculationInstead of higher rates, suppose the speculator expects rates on 5-year high quality bonds to be lower one year from now.

    In this case, her strategy would be to buy a receiver swaption.

  • *Swaptions: SpeculationIf she bought a receiver swaption similar in terms to the above payer swaption (1-year receiver option on a 5-year, 8%/LIBOR swap), and the swap rate on a 5-year swap were less than 8% on the exercise date, then she would realize a gain from exercising and then either selling the floating-payers position or combining it with a fixed-payers position on a replacement swap.

  • *Swaptions: SpeculationFor example, if the fixed rate on a 5-year par value swap were 7%, the investor would exercise her receiver swaption by taking the 8% floating-rate payers swap and then sell the position to another counterparty.

    With the current swap rate at 7% she would be able to sell the 8% fixed-payers position for $415,830:

    If the swap rate were higher than 8% on the exercise date, then the investor would allow the receiver swaption to expire, losing, in turn, her premium.

  • *Swaptions: Speculation Formally, the value of the 8%/LIBOR receiver swaption at expiration is

    For rates, R, on par value 5-year swaps less than the exercise rate of 8%, the value of the receiver swaption will be equal to the present value of the interest differential times the notional principal on the swap.

    For rates equal to or greater than 8%, the swap is worthless.

    The next slide shows graphically and in a table the values and profits at expiration obtained from closing the receiver swaption on the 5-year 8%/LIBOR swap given different rates at expiration.

  • *Value and Profit at Expiration from 8%/LBOR Receiver Swaption

    5.2-1

    123456

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedNet Interest Received

    Payer's Payment*Payer's Payment**by Fixed-Rate Payerby Floating-Rate Payer

    Column 3 - Column 4Column 4 - Column 3

    3/1/030.045

    9/1/030.05225000275000-5000050000

    3/1/040.055250000275000-2500025000

    9/1/040.0627500027500000

    3/1/050.06530000027500025000-25000

    9/1/050.0732500027500050000-50000

    3/1/0635000027500075000.0000000001-75000.0000000001

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    5.2-2

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Fixed-Rate PayerFloating-Rate Loan*and LoanAnnualized Rate***

    Column 3 - Column 4Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000-500002250002750000.055

    3/1/040.055250000275000-250002500002750000.055

    9/1/040.0627500027500002750002750000.055

    3/1/050.065300000275000250003000002750000.055

    9/1/050.07325000275000500003250002750000.055

    3/1/0635000027500075000.00000000013500002750000.055

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-3

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Floating-Rate Payer5% Fixed-Rate Loanand LoanAnnualized Rate***

    Column 4 - Column 3Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000500002500002000000.04

    3/1/040.055250000275000250002500002250000.045

    9/1/040.0627500027500002500002500000.05

    3/1/050.065300000275000-250002500002750000.055

    9/1/050.07325000275000-500002500003000000.06

    3/1/06350000275000-75000.00000000012500003250000.065

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-4

    1234

    Closing DatesLIBORfTCash Flow*

    10[f0 - fT]

    9/1/035975000-25000

    3/1/045.59725000

    9/1/04697000025000

    3/1/056.596750050000

    9/1/05796500075000

    f0 = 972,500

    15.3-2

    Swap MaturityTreasury YieldBid Swap Spread (BP)Ask Swap Spread (BP)Fixed Swap Rate SpreadSwap Rate

    2 year4.98%67745.65% - 5.72%5.69%

    3 year5.17%72765.89% - 5.93%5.91%

    4 year5.38%69746.07% - 6.12%6.10%

    5 year5.50%70766.20% - 6.26%6.23%

    15.3-3

    Fixed-Rate Payers Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net Payment

    6/10/025.50%

    12/10/021835.75%627715.068493151559166.66666666768548.4018264841

    6/10/031826.00%624284.931506849581388.88888888942896.0426179605

    12/10/031836.25%627715.06849315161000017715.0684931509

    6/10/041826.50%624284.931506849631944.444444444-7659.512937595

    12/10/041836.75%627715.068493151660833.333333333-33118.2648401825

    6/10/04182624284.931506849682500-58215.0684931506

    Fixed Payment = (.0626)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    15.4-1

    123456

    Maturity in YearsYield on T-NoteSwap Spread (BP)Swap RateZero Coupon RateImplied 1-year Forward Rates5 year4 year3 year2 YEAR1 YEAR

    10.041000.050.050.05600857144.76190476194.76190476190.04761904764.7619047619100

    20.045800.0530.053080.06504564185.05046965475.05046965470.050504696595.2236257615

    30.05700.0570.057290.07511527465.5034601885.5034601880.055034601999.9855305234

    40.055650.06150.0621760.08520902525.901227016484.46350414230.153158346

    50.06620.06620.067469778.295285946799.779338747

    99.5123475678

    Year5-YEAR

    10.050.0066666667

    20.053080.0063121209

    30.057290.0059226445

    40.0621760.059012054578.5622771259189014.321050802

    50.06746970.06147629572.1476546259

    0.1204883495150.70993175180.0007994719

    15.5-1

    Swap: Fixed payer's position on 8%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%802191.78082191876250039691.7808219179864166.666666667903858.4474885840.0901388889

    6/10/031828.00%797808.219178082783611.11111111114197.1080669712884722.222222222898919.3302891930.0901388889

    12/10/031838.25%802191.780821918813333.333333333-11141.5525114153915000903858.4474885850.0901388889

    6/10/041828.50%797808.219178082834166.666666667-36358.4474885844935277.777777778898919.3302891930.0901388889

    12/10/041838.75%802191.780821918864166.666666667-61974.8858447488965833.333333333903858.4474885840.0901388889

    6/10/051829.00%797808.219178082884722.222222222-86914.0030441399985833.333333333898919.3302891930.0901388889

    12/10/051839.25%802191.780821918915000-112808.2191780821016666.66666667903858.4474885840.0901388889

    6/10/061829.50%797808.219178082935277.777777778-137469.5585996961036388.88888889898919.3302891930.0901388889

    12/10/061839.75%802191.780821918965833.333333333-163641.5525114151067500903858.4474885840.0901388889

    6/10/0718210.00%797808.219178082985833.333333333-188025.1141552511086944.44444444898919.3302891930.0901388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    15.5-2

    Swap: Floating payer's position on 9.5%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%952602.739726028762500-190102.739726028902465.753424658712363.013698630.0700684932

    6/10/031828.00%947397.260273973783611.111111111-163786.149162862897534.246575342733748.0974124810.0725684932

    12/10/031838.25%952602.739726028813333.333333333-139269.406392694902465.753424658763196.3470319630.0750684932

    6/10/041828.50%947397.260273973834166.666666667-113230.593607306897534.246575342784303.6529680360.0775684932

    12/10/041838.75%952602.739726028864166.666666667-88436.0730593608902465.753424658814029.6803652970.0800684932

    6/10/051829.00%947397.260273973884722.222222222-62675.0380517505897534.246575342834859.2085235920.0825684932

    12/10/051839.25%952602.739726028915000-37602.7397260276902465.753424658864863.013698630.0850684932

    6/10/061829.50%947397.260273973935277.777777778-12119.4824961949897534.246575342885414.7640791480.0875684932

    12/10/061839.75%952602.739726028965833.33333333313230.5936073057902465.753424658915696.3470319630.0900684932

    6/10/0718210.00%947397.260273973985833.33333333338436.0730593606897534.246575342935970.3196347030.0925684932

    Fixed Payment = (.095)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    15.5-3

    Swap: Floating payer's position on 5.75%/LIBOR Swap; NP = $1000M; Maturity = 5 years.

    Investment in $1000M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%2882876.712328772287500-595376.7123287682795833.333333333391210.04566210.0676388889

    6/10/031825.00%2867123.287671232401388.88888889-465734.3987823452906944.444444443372678.843226790.0676388889

    12/10/031835.25%2882876.712328772541666.66666667-341210.04566210130500003391210.04566210.0676388889

    6/10/041825.50%2867123.287671232654166.66666667-212956.6210045673159722.222222223372678.843226790.0676388889

    12/10/041835.75%2882876.712328772795833.33333333-87043.37899543483304166.666666673391210.04566210.0676388889

    6/10/051826.00%2867123.287671232906944.4444444439821.156773211434125003372678.843226790.0676388889

    12/10/051836.25%2882876.712328773050000167123.2876712323558333.333333333391210.04566210.0676388889

    6/10/061826.50%2867123.287671233159722.22222222292598.9345509893665277.777777783372678.843226790.0676388889

    12/10/061836.75%2882876.712328773304166.66666667421289.95433789938125003391210.04566210.0676388889

    6/10/071827.00%2867123.287671233412500545376.7123287673918055.555555563372678.843226790.0676388889

    Fixed Payment = (.0575)(no. of days/365)($100,000,000)

    Floating Payment = LIBOR(no. of days/360)($100,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($100,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$100,000,000

    syn fixed swap

    Swap: Fixed payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500139965.753424658864166.6666666671004132.420091320.1001388889

    6/10/031828.00%897534.246575342783611.111111111113923.135464231884722.222222222998645.3576864540.1001388889

    12/10/031838.25%902465.753424658813333.33333333389132.42009132449150001004132.420091320.1001388889

    6/10/041828.50%897534.246575342834166.66666666763367.5799086759935277.777777778998645.3576864540.1001388889

    12/10/041838.75%902465.753424658864166.66666666738299.0867579909965833.3333333331004132.420091320.1001388889

    6/10/051829.00%897534.246575342884722.22222222212812.0243531204985833.333333333998645.3576864530.1001388889

    12/10/051839.25%902465.753424658915000-12534.24657534241016666.666666671004132.420091320.1001388889

    6/10/061829.50%897534.246575342935277.777777778-37743.53120243531036388.88888889998645.3576864530.1001388889

    12/10/061839.75%902465.753424658965833.333333333-63367.579908675610675001004132.420091320.1001388889

    6/10/0718210.00%897534.246575342985833.333333333-88299.08675799081086944.44444444998645.3576864540.1001388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    syn var

    Swap: Floating payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500-139965.753424658902465.7534246587625000.075

    6/10/031828.00%897534.246575342783611.111111111-113923.135464231897534.246575342783611.1111111110.0775

    12/10/031838.25%902465.753424658813333.333333333-89132.4200913244902465.753424658813333.3333333330.08

    6/10/041828.50%897534.246575342834166.666666667-63367.5799086759897534.246575342834166.6666666670.0825

    12/10/041838.75%902465.753424658864166.666666667-38299.0867579909902465.753424658864166.6666666670.085

    6/10/051829.00%897534.246575342884722.222222222-12812.0243531204897534.246575342884722.2222222220.0875

    12/10/051839.25%902465.75342465891500012534.2465753424902465.7534246589150000.09

    6/10/061829.50%897534.246575342935277.77777777837743.5312024353897534.246575342935277.7777777780.0925

    12/10/061839.75%902465.753424658965833.33333333363367.5799086756902465.753424658965833.3333333330.095

    6/10/0718210.00%897534.246575342985833.33333333388299.0867579908897534.246575342985833.3333333330.0975

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    Synfixinv

    Swap: Floating payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment in $20M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500-144143.835616438559166.666666667703310.5022831050.0701388889

    6/10/031825.00%598356.164383562480277.777777778-118078.386605784581388.888888889699467.2754946730.0701388889

    12/10/031835.25%601643.835616438508333.333333333-93310.502283105610000703310.5022831050.0701388889

    6/10/041825.50%598356.164383562530833.333333333-67522.8310502284631944.444444444699467.2754946730.0701388889

    12/10/041835.75%601643.835616438559166.666666667-42477.1689497718660833.333333333703310.5022831050.0701388889

    6/10/051826.00%598356.164383562581388.888888889-16967.2754946728682500699467.2754946730.0701388889

    12/10/051836.25%601643.8356164386100008356.1643835615711666.666666667703310.5022831050.0701388889

    6/10/061826.50%598356.164383562631944.44444444433588.2800608827733055.555555556699467.2754946730.0701388889

    12/10/061836.75%601643.835616438660833.33333333359189.4977168948762500703310.5022831050.0701388889

    6/10/071827.00%598356.16438356268250084143.8356164383783611.111111111699467.2754946730.0701388889

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$20,000,000

    synflinvoat

    Swap: Fixed payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment of $20M in 5-year bond 7%. Synthetic fixed-rate investment: Fixed Investment and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Payer's Net PaymentFixed Investment ReturnFixed Inv Return - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500144143.835616438701917.808219178557773.972602740.055625

    6/10/031825.00%598356.164383562480277.777777778118078.386605784698082.191780822580003.8051750380.0581597222

    12/10/031835.25%601643.835616438508333.33333333393310.502283105701917.808219178608607.3059360730.0606944444

    6/10/041825.50%598356.164383562530833.33333333367522.8310502284698082.191780822630559.3607305930.0632291667

    12/10/041835.75%601643.835616438559166.66666666742477.1689497718701917.808219178659440.6392694060.0657638889

    6/10/051826.00%598356.164383562581388.88888888916967.2754946728698082.191780822681114.9162861490.0682986111

    12/10/051836.25%601643.835616438610000-8356.1643835615701917.808219178710273.972602740.0708333333

    6/10/061826.50%598356.164383562631944.444444444-33588.2800608827698082.191780822731670.4718417050.0733680556

    12/10/061836.75%601643.835616438660833.333333333-59189.4977168948701917.808219178761107.3059360730.0759027778

    6/10/071827.00%598356.164383562682500-84143.8356164383698082.191780822782226.027397260.0784375

    Fixed Payment = (.06)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Investment Return = 7%(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Inv Return - Swap Payment)(365/no. of days)/$20,000,000

    Put-call Parity

    Values at Expiration of Put Swaption and Synthetic Put Swaption consisting of Call Swaption and Forward Contract

    Swap Rates on 2-Year Generic Swap6%7%8%

    Long Put Swaption: Right to pay 7%/receive LIBOR00PV(8%-7%)

    Long Call Swaption: Right to Receive 7%/pay LIBORPV(7%-6%)00

    Swap from Forward: Pay 7%/Receive LIBORPV(6%-7%)PV(7%-7%)PV(8%-7%)

    Net Value00PV(8%-7%)

    PV = present value of two-year cash flows

    Exhibit17.4-1

    Rates on 5-year Par ValuePut Swaption'sValue of 8%/LIBORPut SwaptionProfit from Put

    Swaps at ExpirationInterest DifferentialPut Swaption at ExpiationCostSwaption

    RMax((R-.08)/2,0)PV(Max[(R-.08)/2, 0]($10M))

    0.0600.000050000-50000

    0.0650.000050000-50000

    0.0700.000050000-50000

    0.0750.000050000-50000

    0.0800.000050000-50000

    0.0850.00320027250000150272

    0.0900.00539563650000345636

    0.0950.00858622650000536226

    0.1000.01077217350000722173

    Exhibit17.4-1

    Rates

    Profit

    eXHIBIT17.4-2

    Rates on 5-year Par ValueReceiver Swaption'sValue of 8%/LIBORReceiver SwaptionProfit from

    Swaps at ExpirationInterest DifferentialReceiver Swaption at ExpiationCostReceiver Swaption

    RMax((.08-R)/2,0)PV(Max[(.08R)/2, 0]($10m))

    0.0600.0100$853,020$50,000$803,020

    0.0650.0075$631,680$50,000$581,680

    0.0700.0050$415,830$50,000$365,830

    0.0750.0025$205,320$50,000$155,320

    0.0800.0000$0$50,000-$50,000

    0.0850.0000$0$50,000-$50,000

    0.0900.0000$0$50,000-$50,000

    0.0950.0000$0$50,000-$50,000

    0.1000.0000$0$50,000-$50,000

    eXHIBIT17.4-2

    Rates

    Profit

    16.6-5

    123456

    Year$ CF (millions) CF (millions)Forward Exchange: /BP$ Cost of Sterling (millions)Net $ Revenue (millions)

    Column (4) X Column (3)Column (2) - Column (5)

    10.60.7140.7163550.511477470.08852253

    20.60.7140.733090.523426260.07657374

    30.60.7140.750220.535657080.06434292

    40.60.7140.767750.54817350.0518265

    50.60.7140.7856870.5609805180.039019482

    0.320285172

    16.6-2

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    NOTE THAT THESE CHANGES ARE LIKELY TO CHANGE TOGETHER

    16.6-3

    YearRateCouponBP rateBP BondERU.S. RateGB RateEo = $/$ Value of Swap (millions)$ Value of Swap (millions)

    10.1109.09090909090.0810.7142759.9206250.690.70277777782.4702456252.2456778409$ Received/ Paid Received/$ Paid

    20.1108.26446280990.0810.7142759.18576388890.690.71579218112.33080572921.92628572660.10.0750.700

    30.1107.5131480090.0810.7142758.50533693420.690.72904759182.1887836131.64446552440.0950.0750.71.91995-1.91995

    40.1106.83013455370.0810.7142757.87531197610.690.74254847322.04413145771.39616929020.1050.0750.7-1.87131.8713

    50.111068.30134553650.08153.571275104.5180293120.690.7562993708-6.1458586573-3.81609468880.10.070.7-2.052.05

    100140.0050671112Swap Value3.3965036933Value3.39650369330.10.080.71.99645-1.99645

    0.10.0750.725-1.50371.5037

    0.10.0750.693.3965-3.3965

    ch17prob31

    123456

    Year$ CF (millions) CF (millions)Forward Exchange: /BP$ Cost of Sterling (millions)Net $ Revenue (millions)

    Column (4) X Column (3)Column (2) - Column (5)

    10.857142-0.51.46194780.73097390.12617

    20.857142-0.51.49610550.748052750.10909

    30.857142-0.51.53106120.76553060.09161

    40.857142-0.51.56683360.78341680.07373

    50.857142-0.51.60344190.801720950.05542

    0.45602

    MBD000B2C9E.unknown

    Chart1

    803020.283677583

    581679.631033639

    365830.266128897

    155319.681291995

    -50000

    -50000

    -50000

    -50000

    -50000

    Rates

    Profit

    5.2-1

    123456

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedNet Interest Received

    Payer's Payment*Payer's Payment**by Fixed-Rate Payerby Floating-Rate Payer

    Column 3 - Column 4Column 4 - Column 3

    3/1/030.045

    9/1/030.05225000275000-5000050000

    3/1/040.055250000275000-2500025000

    9/1/040.0627500027500000

    3/1/050.06530000027500025000-25000

    9/1/050.0732500027500050000-50000

    3/1/0635000027500075000.0000000001-75000.0000000001

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    5.2-2

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Fixed-Rate PayerFloating-Rate Loan*and LoanAnnualized Rate***

    Column 3 - Column 4Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000-500002250002750000.055

    3/1/040.055250000275000-250002500002750000.055

    9/1/040.0627500027500002750002750000.055

    3/1/050.065300000275000250003000002750000.055

    9/1/050.07325000275000500003250002750000.055

    3/1/0635000027500075000.00000000013500002750000.055

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-3

    12345678

    SwapSwapSwapLoanSynthetic LoanSynthetic Loan

    Effective DatesLIBORFloating-RateFixed-RateNet Interest ReceivedInterest Paid onPayment on SwapEffective

    Payer's Payment*Payer's Payment**by Floating-Rate Payer5% Fixed-Rate Loanand LoanAnnualized Rate***

    Column 4 - Column 3Column 6 - Column 5

    3/1/030.045

    9/1/030.05225000275000500002500002000000.04

    3/1/040.055250000275000250002500002250000.045

    9/1/040.0627500027500002500002500000.05

    3/1/050.065300000275000-250002500002750000.055

    9/1/050.07325000275000-500002500003000000.06

    3/1/06350000275000-75000.00000000012500003250000.065

    * (LIBOR/2)($10,000,000)

    ** (.055/2)*($10,000,000)

    *** 2 (Payment on Swap and Loan)/$10,000,000

    5.2-4

    1234

    Closing DatesLIBORfTCash Flow*

    10[f0 - fT]

    9/1/035975000-25000

    3/1/045.59725000

    9/1/04697000025000

    3/1/056.596750050000

    9/1/05796500075000

    f0 = 972,500

    15.3-2

    Swap MaturityTreasury YieldBid Swap Spread (BP)Ask Swap Spread (BP)Fixed Swap Rate SpreadSwap Rate

    2 year4.98%67745.65% - 5.72%5.69%

    3 year5.17%72765.89% - 5.93%5.91%

    4 year5.38%69746.07% - 6.12%6.10%

    5 year5.50%70766.20% - 6.26%6.23%

    15.3-3

    Fixed-Rate Payers Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net Payment

    6/10/025.50%

    12/10/021835.75%627715.068493151559166.66666666768548.4018264841

    6/10/031826.00%624284.931506849581388.88888888942896.0426179605

    12/10/031836.25%627715.06849315161000017715.0684931509

    6/10/041826.50%624284.931506849631944.444444444-7659.512937595

    12/10/041836.75%627715.068493151660833.333333333-33118.2648401825

    6/10/04182624284.931506849682500-58215.0684931506

    Fixed Payment = (.0626)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    15.4-1

    123456

    Maturity in YearsYield on T-NoteSwap Spread (BP)Swap RateZero Coupon RateImplied 1-year Forward Rates5 year4 year3 year2 YEAR1 YEAR

    10.041000.050.050.05600857144.76190476194.76190476190.04761904764.7619047619100

    20.045800.0530.053080.06504564185.05046965475.05046965470.050504696595.2236257615

    30.05700.0570.057290.07511527465.5034601885.5034601880.055034601999.9855305234

    40.055650.06150.0621760.08520902525.901227016484.46350414230.153158346

    50.06620.06620.067469778.295285946799.779338747

    99.5123475678

    Year5-YEAR

    10.050.0066666667

    20.053080.0063121209

    30.057290.0059226445

    40.0621760.059012054578.5622771259189014.321050802

    50.06746970.06147629572.1476546259

    0.1204883495150.70993175180.0007994719

    15.5-1

    Swap: Fixed payer's position on 8%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%802191.78082191876250039691.7808219179864166.666666667903858.4474885840.0901388889

    6/10/031828.00%797808.219178082783611.11111111114197.1080669712884722.222222222898919.3302891930.0901388889

    12/10/031838.25%802191.780821918813333.333333333-11141.5525114153915000903858.4474885850.0901388889

    6/10/041828.50%797808.219178082834166.666666667-36358.4474885844935277.777777778898919.3302891930.0901388889

    12/10/041838.75%802191.780821918864166.666666667-61974.8858447488965833.333333333903858.4474885840.0901388889

    6/10/051829.00%797808.219178082884722.222222222-86914.0030441399985833.333333333898919.3302891930.0901388889

    12/10/051839.25%802191.780821918915000-112808.2191780821016666.66666667903858.4474885840.0901388889

    6/10/061829.50%797808.219178082935277.777777778-137469.5585996961036388.88888889898919.3302891930.0901388889

    12/10/061839.75%802191.780821918965833.333333333-163641.5525114151067500903858.4474885840.0901388889

    6/10/0718210.00%797808.219178082985833.333333333-188025.1141552511086944.44444444898919.3302891930.0901388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    15.5-2

    Swap: Floating payer's position on 9.5%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%952602.739726028762500-190102.739726028902465.753424658712363.013698630.0700684932

    6/10/031828.00%947397.260273973783611.111111111-163786.149162862897534.246575342733748.0974124810.0725684932

    12/10/031838.25%952602.739726028813333.333333333-139269.406392694902465.753424658763196.3470319630.0750684932

    6/10/041828.50%947397.260273973834166.666666667-113230.593607306897534.246575342784303.6529680360.0775684932

    12/10/041838.75%952602.739726028864166.666666667-88436.0730593608902465.753424658814029.6803652970.0800684932

    6/10/051829.00%947397.260273973884722.222222222-62675.0380517505897534.246575342834859.2085235920.0825684932

    12/10/051839.25%952602.739726028915000-37602.7397260276902465.753424658864863.013698630.0850684932

    6/10/061829.50%947397.260273973935277.777777778-12119.4824961949897534.246575342885414.7640791480.0875684932

    12/10/061839.75%952602.739726028965833.33333333313230.5936073057902465.753424658915696.3470319630.0900684932

    6/10/0718210.00%947397.260273973985833.33333333338436.0730593606897534.246575342935970.3196347030.0925684932

    Fixed Payment = (.095)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    15.5-3

    Swap: Floating payer's position on 5.75%/LIBOR Swap; NP = $1000M; Maturity = 5 years.

    Investment in $1000M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%2882876.712328772287500-595376.7123287682795833.333333333391210.04566210.0676388889

    6/10/031825.00%2867123.287671232401388.88888889-465734.3987823452906944.444444443372678.843226790.0676388889

    12/10/031835.25%2882876.712328772541666.66666667-341210.04566210130500003391210.04566210.0676388889

    6/10/041825.50%2867123.287671232654166.66666667-212956.6210045673159722.222222223372678.843226790.0676388889

    12/10/041835.75%2882876.712328772795833.33333333-87043.37899543483304166.666666673391210.04566210.0676388889

    6/10/051826.00%2867123.287671232906944.4444444439821.156773211434125003372678.843226790.0676388889

    12/10/051836.25%2882876.712328773050000167123.2876712323558333.333333333391210.04566210.0676388889

    6/10/061826.50%2867123.287671233159722.22222222292598.9345509893665277.777777783372678.843226790.0676388889

    12/10/061836.75%2882876.712328773304166.66666667421289.95433789938125003391210.04566210.0676388889

    6/10/071827.00%2867123.287671233412500545376.7123287673918055.555555563372678.843226790.0676388889

    Fixed Payment = (.0575)(no. of days/365)($100,000,000)

    Floating Payment = LIBOR(no. of days/360)($100,000,000)

    FRN Return = (LIBOR + 1%)(no. of days/360)($100,000,000)

    Annualized Rate = (FRN - Swap Payment)(365/no. of days)/$100,000,000

    syn fixed swap

    Swap: Fixed payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year FRN paying LIBOR + 100 BP. Synthetic Fixed: FRN and Fixed-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFixed Net PaymentFRN PaymentFRN + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500139965.753424658864166.6666666671004132.420091320.1001388889

    6/10/031828.00%897534.246575342783611.111111111113923.135464231884722.222222222998645.3576864540.1001388889

    12/10/031838.25%902465.753424658813333.33333333389132.42009132449150001004132.420091320.1001388889

    6/10/041828.50%897534.246575342834166.66666666763367.5799086759935277.777777778998645.3576864540.1001388889

    12/10/041838.75%902465.753424658864166.66666666738299.0867579909965833.3333333331004132.420091320.1001388889

    6/10/051829.00%897534.246575342884722.22222222212812.0243531204985833.333333333998645.3576864530.1001388889

    12/10/051839.25%902465.753424658915000-12534.24657534241016666.666666671004132.420091320.1001388889

    6/10/061829.50%897534.246575342935277.777777778-37743.53120243531036388.88888889998645.3576864530.1001388889

    12/10/061839.75%902465.753424658965833.333333333-63367.579908675610675001004132.420091320.1001388889

    6/10/0718210.00%897534.246575342985833.333333333-88299.08675799081086944.44444444998645.3576864540.1001388889

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    FRN Payment = (LIBOR + 100BP)(no. of days/360)($20,000,000)

    Annualized Rate = (FRN + Swap Payment)(365/no. of days)/$20,000,000

    syn var

    Swap: Floating payer's position on 9%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    $20M, 5-year, 9% fixed rate loan. Synthetic Variable: Fixed Rate Loan and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFixed-Rate PaymentFixed rate + Swap PaymentAnnualized Rate

    6/10/027.50%

    12/10/021837.75%902465.753424658762500-139965.753424658902465.7534246587625000.075

    6/10/031828.00%897534.246575342783611.111111111-113923.135464231897534.246575342783611.1111111110.0775

    12/10/031838.25%902465.753424658813333.333333333-89132.4200913244902465.753424658813333.3333333330.08

    6/10/041828.50%897534.246575342834166.666666667-63367.5799086759897534.246575342834166.6666666670.0825

    12/10/041838.75%902465.753424658864166.666666667-38299.0867579909902465.753424658864166.6666666670.085

    6/10/051829.00%897534.246575342884722.222222222-12812.0243531204897534.246575342884722.2222222220.0875

    12/10/051839.25%902465.75342465891500012534.2465753424902465.7534246589150000.09

    6/10/061829.50%897534.246575342935277.77777777837743.5312024353897534.246575342935277.7777777780.0925

    12/10/061839.75%902465.753424658965833.33333333363367.5799086756902465.753424658965833.3333333330.095

    6/10/0718210.00%897534.246575342985833.33333333388299.0867579908897534.246575342985833.3333333330.0975

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Floating Payment = LIBOR(no. of days/360)($20,000,000)

    Fixed Payment = (.09)(no. of days/365)($20,000,000)

    Annualized Rate = (Fixed Rate + Swap Payment)(360/no. of days)/$20,000,000

    Synfixinv

    Swap: Floating payer's position on 6%/LIBOR Swap; NP = $20M; Maturity = 5 years.

    Investment in $20M, 5-year, FRN paying LIBOR plus 100 BP. Synthetic fixed-rate investment: FRN Investment and Floating-Payer's Position

    Settlement DateNumber of DaysLIBORFixed PaymentFloating PaymentFloating Payer's Net PaymentFRN ReturnFixed rate - Swap PaymentAnnualized Rate

    6/10/024.50%

    12/10/021834.75%601643.835616438457500-144143.835616438559166.666666667703310.5022831050.0701388889

    6/10/031825.00%598356.164383562480277.777777778-118078.386605784581388.888888889699467.2754946730.0701388889

    12/10/031835.25%601643.835616438508333.333333333-93310.502283105610000703310.5022831050.0701388889

    6/10/041825.50%598356.164383562530833.333333333-67522.8310502284631944.444444444699467.2754946730.0701388889

    12/10/041835.75%601643.835616438559166.666666667-42477.1689497718660833.333333333703310.5022831050.0701388889

    6/10/051826.00%598356.164383562581388.888888889-16967.2754946728682500699467.2754946730.0701388889

    12/10/051836.25%601643.8356164386100008356.1643835615711666.666666667703310.5022831050.0701388889

    6/10/061826.50%598356.164383562631944.44444444433588.2800608827733055.555555556699467.2754946730.0701388889

    12/10/061836.75%601643.835616438660833.33333333359189.4977168948762500703310.5022831050.0701388889

    6/10/071827.00%598356.164383562