© K.Cuthbertson and D.Nitzsche 1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK...

© K.Cuthbertson and D.Nitzsche1

Version 1/9/2001

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

K. Cuthbertson and D. Nitzsche

LECTURE

Foreign Currency Options


Contracts and Payoffs

Hedging Foreign Currency Receiptsusing Forwards, Options and Futures

Pricing Foreign Currency Options

Topics


Contracts and Payoffs


Foreign Currency Options Contracts

Table : Foreign Currency Options PHSE

Contract Size K- Increments Min Price Chge

GBP £31,250 $0.0250 $0.0001 = $3.125

DM DM62,500 $0.050 0.0001 = $6.25

JY JY6,250,000 $0.050 0.000001 = $6.25

Can $ CD50,000 $0.050 0.0001 = $5.00Hold, TVS0 = $2m in diversified equity portfolio and ‘


Fig11.2:Long , Foreign Currency Call

ST

Profit

Strike price K = $140

6

C = 4

$150$144K = $1400

0+1


= Max(ST – K, 0) - C = -C if ST < K = ST - K - C if ST > K

Break even spot rate is:ST,BE = K + C

zop = £31,250 at expiryK = 1.40 $/£ C = 4.0 cents/£ = 0.04 $/£ST = 1.50($/£) (see figure 11.2): Gross profit = (ST – K) zop = (1.50 – 1.40) £31,250 = $3,125

Invoice price per contract = zop C = £31,250 (0.04($/£)) = $1,250

Net profit: = (ST - K – C) £31,250 = (1.50($/£) - 1.40($/£) - 0.04($/£)) £31,250 = (0.06($/£))(£31,250) = $1,875

PROFIT FROM A LONG CALL


Fig 11.3 : Long, Foreign Currency Put

Strike price K = $144

ST

Profit

1.50

P = -2.50

$141.50

$140 K = $1440

0-1


Profit from Long Put

If ST < K 140 < 144

Exercise the option (“in-the-money”)

Gross profit = ( K - ST ) z = (1.44-1.40) 31,250 = $1250

Net profit = (K - ST - P) z = 1.44-1.40-0.025 = $468.75 per contract

If ST > K

Do not exercise the option (out-of-the-money)

Loss = (2.5/100) x 31,250 = $781.25

Loss is limited to put premium (insurance)


Buy (long) call on sterling if you expect sterling to appreciate.

Buy long put on sterling if you expect sterling to depreciate

Calls and Puts: Speculation


Hedging Foreign Currency Receiptsusing

Forwards, Optionsand Futures


Hedging Foreign Currency (Intuition)

US firm makes bid for UK contract, outcome of bid is unknownReceipt of f.c. (GBP) is uncertain

FORWARD/FUTURES MARKETBid successful ~ you are hedged

Bid unsuccessful ~ you are not hedged outcome is unfavourable if sterling appreciates ~ have to buy GBP at ‘high’ rate in spot market, to honour delivery in the f.c.


Hedging Foreign Currency (Intuition)

LONG PUT ON GBP

Bid successful and GBP appreciates ~ outcome favourable even though put expires worthless, as you sell GBP at ‘high’ rate

Bid successful and GBP depreciates ~ outcome ‘favourable’ as you exercise the put and receive K

Bid unsuccessful and GBP appreciates ~ loss limited to the put premium, P

Bid unsuccessful and GBP depreciates ~ outcome ‘favourable’ as you exercise the put and receive (K-ST) - P


US firm :bid for sterling contract, V= £12.5mAt F0 = 1.61($/£), USD equivalent of$20.125m.

PUT CONTRACTStrike Price K = 1.60 ($/£)Size of Contract, zp = £31,250Put Premium P = 0.025 ($/£)Cost, one Put contract (= zpP) = $781.25

Number of Put Contracts NP = (V/zp) = (£12.5m / £31,250) = 400 contracts

Cost of Np puts = Np (zp P) = VP = $312,500 (Note that V = Np zp )

Hedging Foreign Currency Receipts: Detail


Possible outcomes

ST = 1.65($/£) or ST = 1.50($/£)

Bid Successful or Unsuccessful

Hedging Foreign Currency Receipts: Detail


A: Bid Successful (appreciation £)

ST= 1.65

No Hedge

= V.ST =(12.5m)1.65= $20.625m

Forward Market at F0=1.62

= V.F0=(12.5m)(1.61) = $20.125m

Put Option

ST >K, puts not exercised convert £’s at 1.65:

= Spot revenue - Cost of Put

V.ST – Np (zp.P)= V ( ST – P )

= 12.5 (1.65 – 0.025) =$20,312,500Equivalent to Long put + long spot = long call


B: Bid Successful(depreciation £)

ST = 1.50

No Hedge

= V.ST =(£12.5)1.50 = $18.75m


= V. F0 =£12.5(1.61) = $20.125m

Put Option : Exercise Puts (locked in K= 160):

Payoff from puts+long spot - cost of puts

= = [(K - ST) + ST] .V – Np (zp P)

= K .V – Np (zp P) = 1.60 (12.5m) - $312,500

= $19,687,500 Had you chosen put with K = 161 then the put would have a gross payoff

equal to that of the forward.


C: Bid Unsuccessful (appreciation £)

ST = 1.65

No Hedge: No Cash Flow


Purchase £12.5m at a cost of ST = 1.65 and receive F0 =1.61

=(Fo – ST).V == (1.61 – 1.65) £12.5= - $500,000

(Equivalent to open short position in the F.C. and you are exposed to potential large losses as S increases)

Put Option :Not Exercised:(equiv to naked put)

Lost put premium = Np (zp P) = V. P = $312,500


D: Bid Unsuccessful (depreciation £)

ST = 1.50

No Hedge: No Cash Flow


Purchase £12.5m at a cost of ST = 1.50 and

receive F0 =1.62 on (£12.5m)

=(Fo – ST)V == (1.61 – 1.50) £12.5= $1.375m

(Equivalent to open short position in the F.C. and you have potential large gains as S increases)

Put Option : Exercise Puts:(equiv to naked put)

Purchase, at ST= 1.50 and exercise puts K = 1.60

= (K - ST – P ) V=(1.60– 1.50 –0.025) 12.5 = $937,500


Bid Successful = V S1 + V (Fo – F1) = V [F0 + (S1 – F1)]

Bid Unsuccessful = V (Fo – F1)

The outcomes are the same as for the forward market if the futures are held to maturity, F1 = S1 (and ‘close’, if futures are closed out and basis is small)

Hedging: Using Futures


Pricing Foreign Currency Options


Pricing

Replace q= dividend yield by rf

[11.13] C = S N(d1) - K N(d2) [11.14] P = K N(-d2) - S N(-d1)

d1 =

d2 = = d1 -

S is measured as $ per £ (or cents per £),

T

TrrKS fd

)2/()/ln( 2

T

TrrKS fd

)2/()/ln( 2

T


Pricing: Alternative Representation

[11.16] S = F

Substituting [11.16] in [11.13] and [11.14]::

[11.17] C = [F N(d1) - K N(d2)]

[11.18] P = [K N(-d2) – F N(-d1)]

d1 =

d2 =

Trr fde )(

T

TKF

)2/()/ln( 2

T

TKF

)2/()/ln( 2


Table 11.5: Put-Call Parity: Currency Options

Case : ST > K Case : ST < K

Portfolio A(1): Cash ST ST

Long Put 0 K-ST

Total A ST---------------------------- K

Portfolio B(2): Long Call ST - K 0

US T-bond K K

Total A ST------------------------- K

Portfolio A = One long put, plus cash of $A = S0

invested in a foreign bond

Portfolio B = One long call, plus domestic (US) bond of ($) K

Tfre

Tdre

Returns from Two Portfolios :


END OF SLIDES

© K.Cuthbertson and D.Nitzsche 1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK...

Documents

Transcript of © K.Cuthbertson and D.Nitzsche 1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK...