http:// pluto.huji.a c.il/ ~mswiener/ 972-2-588-3049 FRM Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/ ~mswiener/zvi.html Swaps
Dec 19, 2015
http://pluto.huji.ac.il/~mswiener/zvi.html
972-2-588-3049FRM
Zvi Wiener
02-588-3049http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Swaps
Zvi Wiener slide 2Credit Derivatives
Interest Rate Swaps: Concept
• An agreement between 2 parties to exchange periodic payments calculated on the basis of specified interest rates and a notional amount.
•Plain Vanilla Swap
A BFixed rate
Floating rate
Based on a presentation of Global Risk Strategy Group of Deutsche Bank
Zvi Wiener slide 3Credit Derivatives
IRS
• In a standard IRS, one leg consists of fixed rate payments and the other depends on the evolution of a floating rate.
• Typically long dated contracts: 2-30 years
• Sometimes includes options, amortization, etc.
• Interest compounded according to different conventions (eg 30/360, Act/Act. Act/360, etc.)
Zvi Wiener slide 4Credit Derivatives
IRS OriginsAAA wants to borrow in floating and BBB wants to borrow in fixed.
Fixed Floating
AAA 7.00% LIBOR+5bps
BBB 8.50% LIBOR+85bps
difference 1.5% 0.8%
Net differential 70bps = 0.7%
Zvi Wiener slide 5Credit Derivatives
Comparative Advantage
Cost of funds for AAA=Libor - 40bp (45bps saved)
Cost of funds for BBB=8.25% (25bps saved)
Swap rate = 7.40%
Swap rate is the fixed rate which is paid against receiving Libor.
AAA BBBLibor
7.4%7.0% Libor+85bp
Zvi Wiener slide 6Credit Derivatives
Basic terms of IRS
• Notional amount
• Fixed rate leg
• Floating rate leg
• Calculated period
• Day count fraction
Zvi Wiener slide 7Credit Derivatives
Basic terms of IRS
• Payer and receiver - quoted relative to fixed interest (i.e. payer = payer of fixed rate)
• buyer = payer, seller =receiver
• Short party = payer of fixed, (buyer)
• Long party = receiver of fixed, (seller)
• Valuation = net value NOT notional!!
Zvi Wiener slide 8Credit Derivatives
Various swaps• Coupon swaps - fixed against floating.
• Basis or Index swaps - exchange of two streams both are computed using floating IR.
• Currency swap - interest payments are denominated in different currencies.
• Asset swap - to exchange interest received on specific assets.
• Term swap maturity more then 2 years.
• Money Market swap - less then 2 years.
Zvi Wiener slide 9Credit Derivatives
Payments
Fixed payment =
(notional)(Fixed rate)(fixed rate day count convention)
Floating payment =
(notional)(Float. rate)(float. rate day count
convention)
Zvi Wiener slide 10Credit Derivatives
Time Value of Money
• present value PV = CFt/(1+r)t
• Future value FV = CFt(1+r)t
• Net present value NPV = sum of all PV
-PV 5 5 5 5 105
55
4
1 )1(
105
)1(
5
rrPV
tt
t
Zvi Wiener slide 11Credit Derivatives
Zvi Wiener slide 12Credit Derivatives
Swap Pricing
A swap is a series of cash flows.
An on-market swap has a Net Present Value
of zero!
PV(Fixed leg) + PV(Floating leg) = 0
Zvi Wiener slide 13Credit Derivatives
Pricing
• Floating leg is equal to notional amount at each day of interest rate settlement (by definition of LIBOR).
• Fixed leg can be valued by standard NPV, since the paid amount is known.
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Forward starting swaps
• interest starts accruing at some date in the future.
• Valuation is similar to a long swap long and a short swap short.
Zvi Wiener slide 17Credit Derivatives
• Zero coupon swap (reinvested payments)
• Amortizing swap (decreasing notional)
• Accreting swap (increasing notional)
• Rollercoaster (variable notional)
Zvi Wiener slide 18Credit Derivatives
Amortizing swap
Decreasing notional affects coupon payments
Zvi Wiener slide 19Credit Derivatives
Unwinding an existing swap
• Enter into an offsetting swap at the
prevailing market rate.
• If we are between two reset dates the
offsetting swap will have a short first period
to account for accrued interest.
• It is important that floating payment dates
match!!
Zvi Wiener slide 20Credit Derivatives
Unwinding
Net of the two offsetting swaps is 2% for the life of the contract. (sometimes novation)
A B8%
LIBOR
A C6%
LIBOR
Zvi Wiener slide 21Credit Derivatives
Risks of Swaps
• Interest rate risk - value of fixed side may change
• Credit risk - default or change of rating of counterparty
• Mismatch risk - payment dates of fixed and floating side are not necessarily the same
• Basis risk and Settlement risk
Zvi Wiener slide 22Credit Derivatives
Credit risk of a swap contract
Default of counterparty (change of rating).
Exists when the value of swap is positive
Frequency of payments reduces the credit risk,
similar to mark to market.
Netting agreements.
Credit exposure changes during the life of a swap.
Zvi Wiener slide 23Credit Derivatives
Duration of a swap
• Fixed leg has a long duration (approximately).
• Short leg has duration about time to reset.
Duration is a measure of price sencitivity to interest rate changes (approximately is equal to average time to payment).
Zvi Wiener slide 24Credit Derivatives
IRS Markets
Daily average volume of trade (notional)
1995 1998 2001
$63B $155B $331B
Zvi Wiener slide 25Credit Derivatives
Mark to market
• daily repricing
• collateral
• adjustments
• reduces credit exposure
Zvi Wiener slide 26Credit Derivatives
Reasons to use swaps by firms
• Lower cost of funds
• Home market effects
• Comparative advantage of highly rated firms
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Zvi Wiener slide 30Credit Derivatives
FRM-GARP 00:47Which one of the following deals has the largest credit exposure for a $1,000,000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk.A. Pay fixed in an interest rate swap for 1 yearB. Sell USD against DEM in a 1 year forward contract.C. Sell a 1-year DEM CapD. Purchase a 1-year Certificate of Deposit
Zvi Wiener slide 31Credit Derivatives
FRM-GARP 00:47Which one of the following deals has the largest credit exposure for a $1,000,000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk.A. Pay fixed in an interest rate swap for 1 yearB. Sell USD against DEM in a 1 year forward contract.C. Sell a 1-year DEM CapD. Purchase a 1-year Certificate of Deposit
Zvi Wiener slide 32Credit Derivatives
Global Derivatives Markets 1999
IR contracts 60,091FRAs 6,775Swaps 43,936Options 9,380FX contracts 14,344Forwards 9,593Swaps 2,444Options 2,307Equity-linked contr. 1,809Forw. and swaps 283Options 1,527Commodity contr. 548Others 11,408
OTC Instruments $88TExchange traded $13.5TIR contracts 11,669Futures 7,914Options 3,756FX contracts 59Futures 37 Options 22Stock-index contr. 1,793Futures 334Options 1,459
Source BIS
World GDP in 99 = 30,000BAll stocks and bonds = 70,000Liquidation value = 2,800B
Zvi Wiener slide 33Credit Derivatives
Global Derivatives Markets 2001
IR contracts 77,513FRAs 7,737Swaps 58,897Options 10,879FX contracts 16,748Forwards 10,336Swaps 3,942Options 2,470Equity-linked contr. 1,881Forw. and swaps 320Options 1,561Commodity contr. 598Others 14,375
OTC Instruments $111TExchange traded $23.5TIR contracts 21,614Futures 9,137Options 12,477FX contracts 89Futures 66 Options 23Stock-index contr. 1,838Futures 295Options 1,543
Source BIS