K.Cuthbertson, D.Nitzsche 1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK MANAGEMENT (J. Wiley, 2001) K. Cuthbertson and D. Nitzsche LECTURE.

K.Cuthbertson, D.Nitzsche 1

Version 1/9/2001

FINANCIAL ENGINEERING:DERIVATIVES AND RISK MANAGEMENT(J. Wiley, 2001)

K. Cuthbertson and D. Nitzsche

LECTURE

Forward and Futures Markets in Foreign Currency


Forward Market in Foreign Currency

Covered Interest Parity

Creating a Synthetic Forward Contract

Foreign Currency Futures

Topics


Forward Market in Foreign Currency


Forward Market

Contract made today for delivery in the future

Forward rate is “price” agreed, today

eg. One -year Forward rate = 1.5 $ / £

Agree to purchase £100 ‘s forward

In 1-year, receive £100

and pay-out $150


Forward Rates (Quotes)

Yen / $ Yen / $

Spot 131.05-131.15

spotspread

0.10

1m forwddiscount

0.01-0.03 spread ondiscount

0.02

1m forwdrate

131.06-131.18

1m forwdspread

0.12

Rule of thumb. Here discount / premium should be added so that: forward spread > spot spread

Premium (discount) % = ( premium / spot rate ) x ( 365 / m )x 100





CIP determines the forward rate F and CIP holds when:

Interest differential (in favour of the UK)

= forward discount on sterling

(or, forward premium on the $)

( rUK - rUS) / ( 1 + rUS ) = ( F - S ) / S


An Example of CIP

The following set of “prices” are consistent with CIP

rUK = 0.11 (11 %) rUS = 0.10 (10 %)

S = 0.666666 £ / $ (I.e. 1.5 $ / £ )

Then F must equal:

F = 0.67272726 £/ $ ie. 1.486486 $ / £


Covered Interest Parity (CIP)

CHECK: CIP equation holds

Interest differential in favour of UK

( rUK - rUS) / ( 1 + rUS ) = (0.11 -0. 10) / 1.10

= 0.0091 (= 0.91%)

Forward premium on the dollar (discount on £)

= ( F - S ) / S = 0.91%


CIP return to investment in US or UK are equal

1) Invest in UK TVuk = £100 (1. 11) = £111

= £A ( 1 + rUK )

2) Invest in US

£100 to $ ( 100 / 0.6666) = $150 At end year $( 100 / 0.6666 )(1.10) = $165

Forward Contract negotiated today

Certain TV (in £s) from investing in USA:

TVus = £ [( 100 / 0.666 ) . (1.10) ] 0.6727 = £111

= £ [ (A / S ) (1 + rUS) ]. F

Hence : TVuk = £111= TVUS = £111


Covered Interest Parity (Algebra/Derivation)

Equate riskless returns ( in £ )

(1) TVuk = £A ( 1 + rUK )

(2) TVus = £ [ ( A / S ) ( 1 + rUS ) ]. F

F = S ( 1 + rUK ) / ( 1 + rUS )

or F / S = ( 1 + rUK ) / ( 1 + rUS )

Subtract “1” from each side:

( F -S ) / S = ( rUK - rUS ) / ( 1 + rUS )

Forward premium on dollar (discount on sterling)

= interest differential in favour of UK

eg. If rUK - rUS = minus1%pa then F will be below S, that is you get less £ per $ in the forward market, than in the spot market. - does this make sense for CIP ?


Bank Calculates Forward Quote

CIP implies, banks quote for F (£/$) is calculated as

F(quote) = S [( 1 + rUK ) / ( 1 + rUS ) ]

If rUK and rUS are relatively constant then

F and S will move together (positive correln)

hence:

For Hedging with Futures

If you are long spot $-assets and fear a fall in the $ then go short (ie.sell) futures on USD


Creating a Synthetic Forward Contract


Creating a Synthetic FX-Forward Contract

Suppose the actual quoted forward rate is: F = 1.5 ($/£)

Consider the cash flows in an actual forward contract

Then reproduce these cash flows using “other assets”, that is the money markets in each country and the spot exchange rate. This is the synthetic forward contract

Since the two sets of cash flows are identical then the actual forward contract must have a “value” or “price” equal to the synthetic forward contract. Otherwise riskless arbitrage (buy low, sell high) is possible.


Actual FX-Forward Contract: Cash Flows

Will receive $150 and pay out £100 at t=1

No “own funds” are used. No cash exchanges hands today ( time t=0)

10

Pay out £100

Receive $150Data: F = 1.5 ($/£)


Using two money markets and the spot FX rateSuppose: ruk = 11%, rus =10%, S = 1.513636 ($/£)Create cash flows equivalent to actual Forward ContractBegin by “creating” the cash outflow of £100 at t=1

Borrow £90.09 at r(UK) = 11%

Switch £90.09 in spot market and lend $136.36

in the US at r(US) =10%.

Note : S = 1.513636$/£ and no “own funds” are used

Receive $150

£100

10

Synthetic Forward Contract: Cash Flows


Synthetic FX-Forward Contract

Borrowed £100/(1+ruk) =£90.09 at t=0

( Pay out £100 at t=1)

Convert to USD [100/(1+ruk) ] S = $136.36 at t=0

Lend in USA and receive [100/(1+ruk) ] S (1+rus)

= $150 at t=1

Synthetic Forward Rate SF:

Rate of exchange ( t=1) = (Receipt of USD) / (Pay out £’s)

= $150 / £100

SF = [100/(1+ruk) ] S (1+rus) / 100

= S (1+rus) / /(1+ruk)

The actual forward rate must equal the synthetic forward rate


Bank Calculates Outright Forward Quote

F(quote) = S [ ( 1 + rus ) / ( 1 + ruk ) ]

Covered interest parity (CIP)

Also Note:

If rus and ruk are relatively constant then

F and S will move together (positive correln)

Hedging

Long spot $’s then go short (ie.sell) futures on $


Bank Quotes “Forward Points”

Forward Points = F - S

= S [ rus - rUK ) / ( 1 + ruk ) ]

The forward points are calculated from S, and the two money market interest rates

Eg. If “forward points” = 10 and S=1.5 then

Outright forward rate F = S +Forward Points

F = 1.5000 + 10 points = 1.5010


Risk Free Arbitrage Profits ( F and SF are different)

Actual Forward Contract with F = 1.4 ($/£) Pay out $140 and receive £100 at t=1

Synthetic Forward(Money Market)

Data: ruk = 11%, rus =10%, S = 1.513636 ($/£) so SF=1.5 ($/£)

Receive $150 and pay out £100

Strategy:

Sell $140 forward, receive £100 at t=1 (actual forward contract)

Borrow £90.09 in UK money market at t=0 (owe £100 at t=1)

Convert £90.09 into $136.36 in spot market at t=0

Lend $136 in US money market receive $150 at t=1(synthetic)

Riskless Profit = $150 - $140 = $10


Speculation in Forward Market

Bank will try and match hedgers in F-mkt to

balance its currency book

Open Position

Suppose bank has forward contract. at F0 = 1.50 $ / £, to

pay out £100,000 and receive $150,000

One year later : ST = 1.52 $ / £

Buy £100,000 spot and pay $152,000

But only receive $150,000 from the f.c.

Loss (or profit) = ST - F0


Foreign Currency Futures


Futures: Contract Specification

Table 4.1 : Contract Specifications IMM Currency Futures(CME)

Size Tick Size [Value] Initial Margin

Margin Maintenance Margin

1 Pound Sterling £62,500 0.02¢ per £[$12.50] $2,000

2 Swiss Franc SF125,000 0.01¢ per SFr $2,000

3 Japanese Yen Y12,500,000 0.01¢ per 100JY[$12.5] $1,500

4 Canadian Dollar CD100,000 0.001 ($/CD)[$100] $900

5 Euro € 125,000 0.01¢ per Euro [$12.50] varies


Futures: Hedging

S0 = spot rate = 0.6700($/SFr)F0 = futures price (Oct. delivery) = 0.6738($/SFr)Contract Size, z = SFr 125,000Tick size, (value) = 0.0001($/SFr) ($12.50)

US ImporterTVS0 = SFr 500,000

Vulnerable to an appreciation of SFr and hence takes a long position in SFr futuresNf = 500,000/125,000 = 4 contracts


Futures: HedgingNet $-cost = Cost in spot market - Gain on futures

= TVS0 S1 - Nf z (F1 – F0) = TVS0 (S1 - F1 + F0) = TVS0 (b1 + F0) = $ 360,000 - $ 23,300 = $ 336,700

Notes: Nfz = TVS0 Hedge “locks in” the futures price at t=0 that is F0, as long as the final basis b1 = S1 - F1 is “small”.Importer pays out $336,700 to receive SFr 500,000 which implies an effective rate of exchange at t=1 of :

[4.14] Net Cost/TVS0= b1 + F0 = 0.6734 ($/SFr)

~close to the initial futures price of F0 = 0.6738($/SFr) the difference being the final basis b1 = -4 ticks.


Slides End Here

K.Cuthbertson, D.Nitzsche 1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK MANAGEMENT (J. Wiley, 2001) K. Cuthbertson and D. Nitzsche LECTURE.

Documents

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