Download presentation

Presentation is loading. Please wait.

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

2
© K.Cuthbertson and D.Nitzsche 2 Contracts and Payoffs Hedging Foreign Currency Receipts using Forwards, Options and Futures Pricing Foreign Currency Options Topics

3
© K.Cuthbertson and D.Nitzsche 3 Contracts and Payoffs

4
© K.Cuthbertson and D.Nitzsche 4 Foreign Currency Options Contracts Table : Foreign Currency Options PHSE ContractSize K- Increments Min Price Chge GBP £31,250 $0.0250$0.0001 = $3.125 DMDM62,500$0.050 0.0001 = $6.25 JY JY6,250,000$0.0500.000001 = $6.25 Can $CD50,000 $0.0500.0001 = $5.00 Hold, TVS 0 = $2m in diversified equity portfolio and ‘

5
© K.Cuthbertson and D.Nitzsche 5 Fig11.2:Long, Foreign Currency Call STST Profit Strike price K = $140 6 C = 4 $150$144 K = $140 0 0 +1

6
© K.Cuthbertson and D.Nitzsche 6 = Max(S T – K, 0) - C = -CifS T < K = S T - K - CifS T > K Break even spot rate is: S T,BE = K + C z op = £31,250 at expiry K = 1.40 $/£ C = 4.0 cents/£ = 0.04 $/£ S T = 1.50($/£) (see figure 11.2): Gross profit = (S T – K) z op = (1.50 – 1.40) £31,250 = $3,125 Invoice price per contract = z op C = £31,250 (0.04($/£)) = $1,250 Net profit: = (S T - K – C) £31,250 = (1.50($/£) - 1.40($/£) - 0.04($/£)) £31,250 = (0.06($/£))(£31,250) = $1,875 PROFIT FROM A LONG CALL

7
© K.Cuthbertson and D.Nitzsche 7 Fig 11.3 : Long, Foreign Currency Put Strike price K = $144 STST Profit 1.50 P = -2.50 $141.50 $140 K = $144 0 0

8
© K.Cuthbertson and D.Nitzsche 8 Profit from Long Put If S T < K140 < 144 Exercise the option (“in-the-money”) Gross profit = ( K - S T ) z = (1.44-1.40) 31,250 = $1250 Net profit = (K - S T - P) z = 1.44-1.40-0.025 = $468.75 per contract If S T > 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)

9
© K.Cuthbertson and D.Nitzsche 9 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

10
© K.Cuthbertson and D.Nitzsche 10 Hedging Foreign Currency Receipts using Forwards, Options and Futures

11
© K.Cuthbertson and D.Nitzsche 11 Hedging Foreign Currency (Intuition) US firm makes bid for UK contract, outcome of bid is unknown Receipt of f.c. (GBP) is uncertain FORWARD/FUTURES MARKET Bid 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.

12
© K.Cuthbertson and D.Nitzsche 12 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-S T ) - P

13
© K.Cuthbertson and D.Nitzsche 13 US firm :bid for sterling contract, V= £12.5m At F 0 = 1.61($/£), USD equivalent of$20.125m. PUT CONTRACT Strike Price K = 1.60 ($/£) Size of Contract, z p = £31,250 Put Premium P = 0.025 ($/£) Cost, one Put contract (= z p P) = $781.25 Number of Put Contracts N P = (V/z p ) = (£12.5m / £31,250) = 400 contracts Cost of N p puts = N p (z p P) = VP = $312,500 (Note that V = N p z p ) Hedging Foreign Currency Receipts: Detail

14
© K.Cuthbertson and D.Nitzsche 14 Possible outcomes S T = 1.65($/£) or S T = 1.50($/£) Bid Successful or Unsuccessful Hedging Foreign Currency Receipts: Detail

15
© K.Cuthbertson and D.Nitzsche 15 A: Bid Successful (appreciation £) S T = 1.65 No Hedge = V.S T =(12.5m)1.65= $20.625m Forward Market at F 0 =1.62 = V.F 0 =(12.5m)(1.61) = $20.125m Put Option S T >K, puts not exercised convert £’s at 1.65: = Spot revenue - Cost of Put V.S T – N p (z p.P)= V ( S T – P ) = 12.5 (1.65 – 0.025) =$20,312,500 Equivalent to Long put + long spot = long call

16
© K.Cuthbertson and D.Nitzsche 16 B: Bid Successful(depreciation £) S T = 1.50 No Hedge = V.S T =(£12.5)1.50 = $18.75m Forward Market at F 0 =1.62 = V. F 0 =£12.5(1.61) = $20.125m Put Option: Exercise Puts (locked in K= 160): Payoff from puts+long spot - cost of puts = = [(K - S T ) + S T ].V – N p (z p P) = K.V – N p (z p 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.

17
© K.Cuthbertson and D.Nitzsche 17 C: Bid Unsuccessful (appreciation £) S T = 1.65 No Hedge: No Cash Flow Forward Market at F 0 =1.62 Purchase £12.5m at a cost of S T = 1.65 and receive F 0 =1.61 =(F o – S T ).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 = N p (z p P) = V. P = $312,500

18
© K.Cuthbertson and D.Nitzsche 18 D: Bid Unsuccessful (depreciation £) S T = 1.50 No Hedge: No Cash Flow Forward Market at F 0 =1.61 Purchase £12.5m at a cost of S T = 1.50 and receive F 0 =1.62 on (£12.5m) =(F o – S T )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 S T = 1.50 and exercise puts K = 1.60 = (K - S T – P ) V=(1.60– 1.50 –0.025) 12.5 = $937,500

19
© K.Cuthbertson and D.Nitzsche 19 Bid Successful = V S 1 + V (F o – F 1 ) = V [F 0 + (S 1 – F 1 )] Bid Unsuccessful = V (F o – F 1 ) The outcomes are the same as for the forward market if the futures are held to maturity, F 1 = S 1 (and ‘close’, if futures are closed out and basis is small) Hedging: Using Futures

20
© K.Cuthbertson and D.Nitzsche 20 Pricing Foreign Currency Options

21
© K.Cuthbertson and D.Nitzsche 21 Pricing Replace q= dividend yield by r f [11.13]C = S N(d 1 ) - K N(d 2 ) [11.14]P = K N(-d 2 ) - S N(-d 1 ) d 1 = d 2 = = d 1 - S is measured as $ per £ (or cents per £),

22
© K.Cuthbertson and D.Nitzsche 22 Pricing: Alternative Representation [11.16]S = F Substituting [11.16] in [11.13] and [11.14]:: [11.17]C = [F N(d 1 ) - K N(d 2 )] [11.18]P = [K N(-d 2 ) – F N(-d 1 )] d 1 = d 2 =

23
© K.Cuthbertson and D.Nitzsche 23 Table 11.5: Put-Call Parity: Currency Options Case : S T > KCase : S T < K Portfolio A (1) : Cash S T S T Long Put 0 K-S T Total A S T---------------------------- K Portfolio B (2) : Long Call S T - K 0 US T-bond K K Total A S T------------------------- K Portfolio A = One long put, plus cash of $A = S 0 invested in a foreign bond Portfolio B = One long call, plus domestic (US) bond of ($) K Returns from Two Portfolios :

24
© K.Cuthbertson and D.Nitzsche 24 END OF SLIDES

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google