1. Chapter 07 Foreign Currency Derivatives 1

2. Foreign currency futures quotation, valuation, and speculation Foreign currency futures and forward contracts Foreign currency option quotation and use Tracking option profits from Buying (long position) and writing (selling or short position) Option valuation 2

3. Foreign Currency Derivatives Derivatives drive their values from the underlying asset They might be used for two distinct management objectives: – Speculation – the financial manager takes a position in the expectation of profit – Hedging – the financial manager uses the instruments to reduce the risks of the corporation’s cash flow In the wrong hands, derivatives can cause a corporation to collapse, but used wisely they allow a financial manager the ability to plan cash flows The derivatives we will consider are: – Foreign Currency Futures – Foreign Currency Options 3

4. Foreign Currency Futures A foreign currency futures contract is an alternative to a forward contract – It calls for future delivery of a standard amount of currency at a fixed time, place, and price – These contracts are traded on exchanges with the largest being the Chicago Mercantile Exchange (CME) Contract Specifications: – Size of contract – called the notional principal, trading in each currency must be done in an even multiple – Method of stating exchange rates – “American terms” are used; quotes are in US dollar cost per unit of foreign currency, also known as direct quotes 4

5. Foreign Currency Futures Contract Specifications – continued – Maturity date – contracts mature on the 3rd Wednesday of January, March, April, June, July, September, October or December – Last trading day – contracts may be traded through the second business day prior to maturity date – Collateral & maintenance margins – the purchaser or trader must deposit an initial margin or collateral At the end of each trading day, the account is marked to market and the balance in the account is either credited if value of contracts is greater or debited if value of contracts is less than account balance 5

6. Foreign Currency Futures Contract Specifications – Settlement – only 5% of futures contracts are settled by physical delivery, most often buyers and sellers offset their position prior to delivery date by taking offsetting positions The complete buy/sell or sell/buy is termed a round turn – Commissions – customers pay a single commission to their broker to execute a round turn – Use of a clearing house as a counterparty – All contracts are agreements between the client and the exchange clearing house. Therefore, there is no counter-party risk 6

7. Using Foreign Currency Futures If an investor wishes to speculate on the movement of a currency can pursue one of the following strategies – Short position – selling a futures contract based on view that currency will fall in value – Long position – purchase a futures contract based on view that currency will rise in value – Example: Amber believes that Mexican peso will fall in value against the US dollar, she looks at quotes in the WSJ for Mexican peso futures 7

8. Using Foreign Currency Futures All contracts are for 500,000 new Mexican pesos. “Open,” “High” and “Low” all refer to the price on the day. “Settle” is the closing price on the day and “Change” indicates the change in the settle price from the previous day. “High” and “Low” to the right of Change indicates the highest and lowest prices for this specific contact during its trading history. “Open Interest” indicates the number of contracts outstanding 8 MaturityOpenHighLowSettleChangeHighLow Open Interest Mar.10953.10988.10930.10958---.11000.0977034,481 June.10790.10795.10778.10773---.10800.097303,405 Sept.10615.10610.10573---.10615.099301,4181

9. Using Foreign Currency Futures Example (cont.): Amber believes that the value of the peso will fall, so she sells a March futures contract By taking a short position on the Mexican peso, Amber locks-in the right to sell 500,000 Mexican pesos at maturity at a set price above their current spot price Using the quotes from the table, Amber sells one March contract for 500,000 pesos at the settle price: $0.10958/Ps Value at maturity (Short position) = – Notional principal × (Spot – Futures) 9

10. Using Foreign Currency Futures To calculate the value of Amber’s position we use the following formula Value at maturity (Short position) = – Notional principal × (Spot – Futures) Using the settle price from the table and assuming a spot rate of $0.09450/Ps at maturity, Amber’s profit is Value = – Ps500,000 × ($0.09450/Ps – $0.10958/Ps) = $7,540 If Amber believed that the Mexican peso would rise in value, she would take a long position on the peso Value at maturity (Long position) = Notional principal × (Spot – Futures) Using the settle price from the table and assuming a spot rate of $0.11500/Ps at maturity, Amber’s profit is Value = Ps500,000 × ($0.11500/Ps – $0.10958/Ps) = $2,710 10

11. Daily Marking-to-Market Value at maturity (Long position) = Notional principal × (Spot – Futures) Value at maturity (Long position) = €125,000 × ($1.2645/€ - $1.2724/€) = -$987.50 11

12. Foreign Currency Futures Versus Forward Contracts 12

13. Foreign Currency Options A foreign currency option is a contract giving the purchaser of the option the right to buy or sell a given amount of currency at a fixed price per unit for a specified time period – The most important part of clause is the “right, but not the obligation” to take an action – Two basic types of options, calls and puts Call – buyer has right to purchase currency Put – buyer has right to sell currency – The buyer of the option is the holder and the seller of the option is termed the writer 13

14. Foreign Currency Options Every option has three different price elements – The strike or exercise price is the exchange rate at which the foreign currency can be purchased or sold – The premium, the cost, price or value of the option itself paid at time option is purchased – Spot exchange rate in the market There are two types of option maturities – American options may be exercised at any time during the life of the option – European options may not be exercised until the specified maturity date 14

15. Foreign Currency Options Options may also be classified as per their payouts – At-the-money (ATM) options have an exercise price equal to the spot rate of the underlying currency – In-the-money (ITM) options may be profitable, excluding premium costs, if exercised immediately – Out-of-the-money (OTM) options would not be profitable, excluding the premium costs, if exercised 15

16. Foreign Currency Options Markets Over-the-Counter (OTC) Market – OTC options are most frequently written by banks for US dollars against British pounds, Swiss francs, Japanese yen, Canadian dollars and the Euro – Main advantage is that they are tailored to purchaser – Counterparty risk exists – Mostly used by individuals and banks Organized Exchanges – similar to the futures market, currency options are traded on an organized exchange floor – The Chicago Mercantile and the Philadelphia Stock Exchange serve options markets – Clearinghouse services are provided by the Options Clearinghouse Corporation (OCC) 16

17. Foreign Currency Options Markets Table shows option prices on British pound taken from the online edition of Wall Street Journal 17

18. Foreign Currency Options Markets The spot rate on the same day was $1.6440/£ The strike price means the price per pound that must be paid if the option is exercised. The February call option of 1620 suggests a strike price of $1.6200/£ The premium, or cost, of the March 1620 option was 2.94 cents per pound or $0.0294 – For a call option on £62,500, the total cost would be £62,500 x $0.0294/£ = $1,837.50 18

19. Foreign Currency Speculation Hans Schmidt is a currency speculator. He is willing to risk his money based on his view of currencies and he may do so in the spot, forward or options market Assume Hans has $100,000 and he believes that the six month spot rate for Swiss francs will be $0.6000/Sfr. Hans thinks that Swiss franc will appreciate or dollar will depreciate. The current spot rate and six-month forward rates are $0.5851/Sfr and $0.5760/Sfr, respectively 19

20. Foreign Currency Speculation Speculating in the spot market – Hans should take the following steps – Use the $100,000 to purchase Sfr170,910.96 today at a spot rate of $0.5851/Sfr – Hold the francs indefinitely, because Hans is in the spot market he is not committed to the six month target – When target exchange rate is reached, sell the Sfr170,910.96 at new spot rate of $0.6000/Sfr, receiving Sfr170,910.96 x $0.6000/Sfr = $102,546.57 – This results in a profit of $2,546.57 or 2.5% ignoring cost of interest income and opportunity costs 20

21. Foreign Currency Speculation Speculating in the forward market – If Hans were to speculate in the forward market, his viewpoint would be that the future spot rate will differ from the forward rate – Today, Hans should purchase Sfr173,611.11 forward six months at the forward quote of $0.5760/Sfr. This step requires no cash outlay – In six months, fulfill the contract receiving Sfr173,611.11 at $0.5760/Sfr at a cost of $100,000 – Simultaneously sell the Sfr173,611.11 in the spot market at Hans’ expected spot rate of $0.6000/Sfr, receiving Sfr173,611.11 x $0.6000/Sfr = $104,166.67 – This results in a profit of $4,166.67 with no investment required and assumes Hans is right 21

22. Foreign Currency Speculation Speculating in the options market – If Hans were to speculate in the options market, his viewpoint would determine what type of option to buy or sell – As a buyer of a call option, Hans purchases the August call on francs at a strike price of $0.5850/Sfr and a premium of $0.0050/Sfr – At spot rates below the strike price, Hans would not exercise his option because he could purchase francs cheaper on the spot market than via his call option 22

23. Long Call Option Speculating in the options market – Hans’ only loss would be limited to the cost of the option, or the premium ($0.0050/Sfr) – At all spot rates above the strike of $0.5850/Sfr Hans would exercise the option, paying only the strike price for each Swiss franc If the franc were at $0.5950/Sfr, Hans would exercise his options buying Swiss francs at $0.5850/Sfr instead of $0.5950/Sfr 23

24. Long Call Option Speculating in the options market – Hans could then sell his Swiss francs on the spot market at $0.5950/Sfr for a profit – At any spot rate, profit from a long call option can be determined by: – Net Profit = Maximum [ (Spot Rate – Strike Price), 0 ] – Premium – Net Profit = Maximum [ ($0.595/Sfr – $0.585/Sfr), 0 ] – $0.005/Sfr – Net Profit = $0.005/Sfr 24

25. Long Call Option Speculating in the options market – Hans could also wait to see if the Swiss franc appreciates more, this is the value to the holder of a call option – limited loss, unlimited upside – Hans’ break-even price can also be calculated by combining the premium cost of $0.005/Sfr with the cost of exercising the option, $0.5850/Sfr This matched the proceeds from exercising the option at a price of $0.5900/Sfr 25

26. Profit & Loss for the Buyer of a Call Option 26 Loss Profit (US cents/SF) + 1.00 + 0.50 0 - 0.50 - 1.00 57.558.059.059.558.5 Limited loss Unlimited profit Break-even price Strike price “Out of the money”“In the money” “At the money” Spot price (US cents/SF) The buyer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited loss of 0.50 cents/SF at spot rates less than 58.5 (“out of the money”), and an unlimited profit potential at spot rates above 58.5 cents/SF (“in the money”).

27. Short Call Option Speculating in the options market – Hans could also write a call, if the future spot rate is below $0.5850/Sfr, then the holder of the option would not exercise it and Hans would keep the premium – If Hans went uncovered and the option was exercised against him, he would have to purchase Swiss francs on the spot market at a higher rate than he is obligated to sell them at – Here the writer of a call option has limited profit and unlimited losses if uncovered 27

28. Profit & Loss for the Writer of a Call Option Speculating in the options market Hans’ payout on writing a call option would be At any spot rate, profit from a short call option can be determined by: – Net Profit = – Maximum [ (Spot Rate – Strike Price), 0 ] + Premium – Net Profit = – Maximum [ ($0.595/Sfr – $0.585/Sfr), 0 ] + $0.005/Sfr – Net Profit = – $0.005/Sfr 28

29. Profit & Loss for the Writer of a Call Option 29 Loss Profit (US cents/SF) + 1.00 + 0.50 0 - 0.50 - 1.00 57.558.059.059.558.5 Limited profit Unlimited loss Break-even price Spot price (US cents/SF) The writer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited profit of 0.50 cents/SF at spot rates less than 58.5, and an unlimited loss potential at spot rates above (to the right of) 59.0 cents/SF. Strike price

30. Long Put Option Speculating in the options market – Hans could also buy a put, the only difference from buying a call is that Hans now has the right to sell currency at the strike price – If the franc drops to $0.575/Sfr Hans will deliver to the writer of the put and receive $0.585/Sfr – The francs can be purchased on the spot market at $0.575/Sfr – With the cost of the option being $0.005/Sfr, Hans realizes a net gain of $0.005/Sfr 30

31. Long Put Option Speculating in the options market Hans’ payout on buying a put option would be At any spot rate, profit from a long put option can be determined by: – Net Profit = Maximum [ (Strike Price – Spot Rate), 0 ] – Premium – Net Profit = Maximum [ ($0.585/Sfr – $0.575/Sfr), 0 ] – $0.005/Sfr – Net Profit = $0.005/Sfr 31

32. Profit & Loss for the Buyer of a Put Option 32 Loss Profit (US cents/SF) + 1.00 + 0.50 0 - 0.50 - 1.00 57.558.059.059.558.5 Limited loss Profit up to 58.0 Strike price “In the money”“Out of the money” “At the money” Spot price (US cents/SF) The buyer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited loss of 0.50 cents/SF at spot rates greater than 58.5 (“out of the money”), and a profit potential at spot rates less than 58.5 cents/SF (“in the money”) up to 58.0 cents. Break-even price

33. Short Put Option Speculating in the options market – And of course, Hans could write a put, thereby obliging him to purchase francs at the strike price – If the franc drops below $0.5800/Sfr Hans will lose more than the premium received – If the spot rate does not fall below $0.5850/Sfr then the option will not be exercised and Hans will keep all the premium from the option 33

34. Short Put Option Speculating in the options market Hans’ payout on writing a put option would be At any spot rate, profit from a short put option can be determined by: – Net Profit = – Maximum [ (Strike Price – Spot Rate), 0 ] + Premium – Net Profit = – Maximum [ ($0.585/Sfr – $0.575/Sfr), 0 ] + $0.005/Sfr – Net Profit = – $0.005/Sfr 34

35. Profit & Loss for the Writer of a Put Option 35 Loss Profit (US cents/SF) + 1.00 + 0.50 0 - 0.50 - 1.00 57.558.059.059.558.5 Loss up to 58.0 Limited profit Strike price Spot price (US cents/SF) The writer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited profit of 0.50 cents/SF at spot rates greater than 58.5, and a loss potential at spot rates less than 58.5 cents/SF up to 58.0 cents. Break-even price

36. Option Pricing and Valuation The pricing of any foreign currency option combines the following: – Domestic risk-free interest rate – Foreign risk-free interest rate – Strike price – Time-to-maturity – Volatility 36

37. Option Pricing and Valuation The intrinsic value is the financial gain if an option is exercised immediately (at-the-money) – This value will reach zero when the option is out-of- the-money – When the spot rate rises above the strike price, the call option will be in-the-money – When the spot rate falls below the strike price, the put option will be in-the-money – At maturity date, the call and put options will have values equal to their intrinsic values 37

38. Valuing a Call Option Assume you have the following information 38

39. Option Pricing and Call Valuation The formula value column (shown on the next slide) is based on the following: 39

40. Option Pricing and Call Valuation 40

41. Option Pricing and Call Valuation 41

42. Valuing a Put Option Assume you have the following information 42

43. Option Pricing and Put Valuation The formula value column (shown on the next slide) is based on the following: 43

44. Option Pricing and Put Valuation 44

45. Option Pricing and Put Valuation 45

46. Option Pricing and Valuation The time value of the option exists because the price of the underlying currency can potentially move further into the money between today and maturity – In the exhibits, time value is shown as the area between formula value and intrinsic value 46

47. Currency Option Pricing Sensitivity Forward rate sensitivity: – Standard foreign currency options are priced around the forward rate because the current spot rate and both the domestic and foreign interest rates are included in the option premium calculation – The option-pricing formula calculates a subjective probability distribution centered on the forward rate – This approach does not mean that the market expects the forward rate to be equal to the future spot rate, it is simply a result of the arbitrage-pricing structure of options 47

48. Currency Option Pricing Sensitivity Spot rate sensitivity (delta or Δ): – The sensitivity of the option premium to a small change in the spot exchange rate is called the delta – The higher the delta, the greater the probability of the option expiring in-the-money – What is the delta of a deep-in the-money call option? – What is the delta of a deep-in the-money put option? – What is the delta of a deep out-of-the money call option? – What is the delta of a deep out-of-the money put option? 48

49. Currency Option Pricing Sensitivity Time to maturity – value and deterioration (theta or θ): – Option values increase with the length of time to maturity – Time value of an option deteriorates as we approach to maturity – This deteriorates is measured by theta – The deteriorates is non-linear, increases at a faster rate as expiration nears – A trader will normally find longer-maturity option better values, giving the trader the ability to alter an option position without suffering significant time value deterioration 49

50. Theta: Option Premium Time Value Deterioration 50 Days remaining to maturity Option Premium (US cents/£) A Call Option on British Pounds: Spot Rate = $1.70/£ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 9080706050403020100 In-the-money (ITM) call ($1.65 strike price) At-the-money (ATM) call ($1.70 strike price) Out-of-the-money (OTM) call ($1.75 strike price)

51. Currency Option Pricing Sensitivity Sensitivity to volatility (lambda or λ): – Option volatility is defined as the standard deviation of daily percentage changes in the underlying exchange rate – An option on a volatile underlying asset is more valuable than a similar option on a less volatile underlying asset – The denominator uses change in the annual volatility 51

52. Currency Option Pricing Sensitivity The primary problem with volatility is that it is unobservable, there is no single correct method for its calculation Thus, volatility is viewed in three ways – Historic – normally measured as the percentage movement in the spot rate on a daily basis, or other time period – Forward-looking – a trader may adjust recent historic volatilities for expected market swings – Implied – calculated by backing out of the market option premium Traders who believe that volatilities will fall significantly in the near-term will sell (write) options now, hoping to buy them back for a profit immediately volatilities fall, causing option premiums to fall. 52

53. Currency Option Pricing Sensitivity Sensitivity to changing interest rate differentials (rho or ρ and phi or φ): – Currency option prices and values are linked to the forward rate Option valuation formula contains spot rate and currency interest rates – The forward rate is in turn based on the theory of Interest Rate Parity – Interest rate changes in either currency will alter the option’s premium or value A trader who is purchasing a call option on foreign currency should do so before the domestic interest rate rises. This timing will allow the trader to purchase the option before its price increases. 53

54. Currency Option Pricing Sensitivity The expected change in the option premium from a small change in the domestic interest rate (home currency) is the term rho. The expected change in the option premium from a small change in the foreign interest rate (foreign currency) is termed phi. 54

55. Interest Differentials and Call Option Premiums 55 Interest differential: i US$ - i £ (percentage) Option Premium (US cents/£) A Call Option on British Pounds: Spot Rate = $1.70/£ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 -4.0-3.0-2.0 01.02.03.04.05.0 ITM call ($1.65 strike price) ATM call ($1.70 strike price) OTM call ($1.75 strike price) 8.0

56. Currency Option Pricing Sensitivity The sixth and final element that is important to option valuation is the selection of the actual strike price. A firm must make a choice as per the strike price it wishes to use in constructing an option (OTC market). Consideration must be given to the tradeoff between strike prices and premiums. 56

57. Option Premiums for Alternative Strike Rates 57 Call strike price (U.S. dollars/£) Option Premium (US cents/£) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 1.661.671.681.69 1.701.711.721.731.741.75 Current spot rate = $1.70/£ OTM Strike rates ITM Strike rates

58. Summary of Option Premium Components 58