Foreign Currency Derivatives Eiteman et al., Chapter 5 Winter 2006
Outline of the Chapter Foreign Currency Futures Currency Options Option Pricing and Valuation Currency Option Pricing Sensitivity Prudence in Practice 2
Foreign Currency Futures A foreign currency futures contract is similar to a forward contract. Futures contracts are standardized: Size of contracts and maturity dates are set by the exchange where the contract is traded. Futures contracts also require daily settlement of gains and losses and have maintenance margin requirements. 3
Foreign Currency Futures Contract specifications (Chicago): Size of the Contract: E125,000, 12,500,000, etc. Method of Stating the Exchange Rate: American terms. Maturity Date: Third Wednesday of January, March, April, June, July, September, October or December. Last Trading Day: Second business day prior to MD. Initial and Maintenance Margins: Contracts are marked to market. 4
Foreign Currency Futures Contract specifications: Settlement: 5% of all futures contracts involve physical delivery. The rest of the time the contract is offset by an opposite position. Commissions: Round trip fees. Clearing House: Ensures liquidity of the contracts. 5
Foreign Currency Futures A trader takes a short position when selling a futures contract, which corresponds to selling the currency forward. A trader takes a long position when buying a futures contract, which corresponds to buying the currency forward. 6
Anatomy of a Futures Trade On Tuesday morning, an investor takes a long position in a Swiss franc futures contract that matures on Thursday afternoon. The agreed-on price is $0.75/SFr and the contract size is SFr125,000. Initial margin requirement is $1,485. Maintenance margin requirement is $1,100. 7
Anatomy of a Futures Trade Tuesday Close Futures price has risen to $0.755. Cash profit of 125, 000 (0.755 0.750) = $625 is deposited into the trader s account (daily settlement). Investor has 1, 485 + 625 = $2, 110 in his account. Existing futures contract at $0.75 is canceled and the investor receives a new futures contract with $0.755 as the prevailing price. 8
Anatomy of a Futures Trade Wednesday Close Futures price has declined to $0.743. Investor s payoff: 125, 000 (0.743 0.755) = $1, 500. Investor s account is debited (daily settlement): 2,110 1,500 = $610 < $1,100. Investor has less than the maintenance margin requirement. If keeping his contract, he receives a margin call of 1,100 610 = $490. 9
Note on Margin Calls Once the amount in the account falls below the maintenance margin requirement, the broker may ask the trader to bring the account value to the initial margin requirement. The minimum margin requirements are set by the exchange. Actual margin requirements set by brokers may be different, as long as they do not fall below the exchange s requirements. 10
Anatomy of a Futures Trade Thursday Close Futures price has declined to $0.74. Investor s payoff: 125, 000 (0.74 0.743) = $375. Investor s net loss on the contract is $1,250 (1,500 + 375-625) before paying commissions. Investor takes delivery of the SFr125,000. A contract can be closed by an offsetting trade. A trader with a long position may offset his trade by taking a short position of equivalent size. 11
Currency Options A foreign currency option is a contract giving the option purchaser (holder) the right, but not the obigation, to buy or sell a given amount of foreign exchange at a fixed price per unit for a specified period of time. Call vs put Holder vs writer 12
Currency Options An American option can be exercised at any time before the maturity date. A European option can be exercised at the maturity date only. The premium, or option price, is the cost of the option. An option is in-the-money if exercising it profitable, excluding the premium cost. It can also be at-the-money or out-of-the-money. 13
Currency Options Foreign Currency Options Markets Over-the-Counter Market 14
Currency Options Quotations and Prices Spot Rate: In $/currency. Exercise Price: In $/currency. Premium: If premium $0.0050/SFr and the contract size is SFr125,000, then the cost of the option is SFr125, 000 $0.0050/SFr = $625.00. 15
Currency Options Let T Expiration date of the option Q Size of the contract S 0 Current spot rate S T Exchange at the option s expiration date X Strike price C Price of a call option P Price of a put option 16
Currency Options Let also π wc Profit to the writer of a call π hc Profit to the holder of a call π wp Profit to the writer of a put π hp Profit to the holder of a put 17
Currency Options π hc 0 C X S T π wc C 0 X S T 18
Currency Options π hp X P π wp 0 P X S T P 0 P X X S T 19
Foreign Currency Speculation Median Joe is a currency speculator. He is willing to risk money based on his view of currencies and he may do so in the spot, forward or options market. Assume Joe has $100,000 and he believes that the six month spot rate for Swiss francs will be $0.6000/SFr. The current spot price for Swiss francs is $0.5851/SFr. 20
Foreign Currency Speculation Speculating in the Spot Market Joe can use the $100,000 to purchase Swiss francs at the rate of $0.5851/SFr, which gives SFr170,910.96, and hold the francs indefinitely. When target rate ($0.6000/SFr) is reached, sell the SFr170,910.96 for $. Profit: 170, 910.96 (0.6000 0.5851) = $2, 546.57 ignoring interest and opportunity costs. 21
Foreign Currency Speculation Speculating in the Forward Market Suppose the six-month forward quote is $0.5760/SFr. Joe can buy a contract for $100,000 (no cash outlay initially). At the contract maturity, Joe expects to sell the 100,000 0.5760 = SFr173,611.11 received at the rate of $0.6000/SFr, for an expected profit of 100, 000 0.5760 0.6000 100,000 = $4,166.67. 22
Foreign Currency Speculation Speculating in the Options Market Joe could buy the August call on francs at a strike price of 58 1 2 ($0.5850/SFr) at a premium of 0.50 or $0.0050/SFr. We re currently in February. Suppose the contract size is SFr125,000. If spot rate is below strike price, Joe won t exercise his options and he will lose 125,000 0.005 = $625 per contract. If spot rate is above 58 1 2, the options will be exercised and Joe s profit per contract will be 125,000 (Spot rate 0.5850 0.0050) = 125,000 (Spot rate 0.5900). 23
Speculating in the Options Market Joe could also write a put option, hoping that it won t be exercised. Letting S, X and P denote the spot price at maturity date, the strike price and the option premium, respectively, his profit at maturity would be π w = P (X S) if S X, P if S > X. 24
Foreign Currency Speculation Speculating in the Options Market If he were expecting the value of SFr to decrease, Joe could write a call option, hoping that it won t be exercised. Letting S, X and C denote the spot price at maturity date, the strike price and the option premium, respectively, his profit at maturity would be π w = C if S X, C (S X) if S > X. 25
Foreign Currency Speculation Speculating in the Options Market If he were expecting the value of SFr to decrease, Joe could buy a put option. Letting S, X and P denote the spot price at maturity date, the strike price and the option premium, respectively, his profit at maturity would be π w = X S P if S X, P if S > X. 26
Synthetic Forward Options can be used to fix the rate at which a currency will be exchanged at a certain date in the future. That is, options can be used to create a synthetic forward contract. Suppose that Joe expects to pay USD1,000,000 in 90 days and suppose the 90-day forward exchange rate is CAD1.1500/USD. 27
Synthetic Forward Joe can fix his 90-day exchange rate at CAD1.1500/USD with a forward contract. He can also fix his exchange rate with options. His options portfolio must then be such that each USD he pays in 90 days costs him CAD1.1500. 28
Synthetic Forward To pay CAD1.1500/USD when the exchange rate is greater than CAD1.1500/USD, he needs a call option with an exercise price of CAD1.1500/USD. To also pay CAD1.1500/USD when the exchange rate falls below CAD1.1500/USD, he needs to write a put option with an exercise price of CAD1.1500/USD. 29
Synthetic Forward Having to pay USD1,000,000 in 90 days, Joe can fix his exchange rate by buying a call and writing a put with the same exercise price of CAD1.1500/USD. There is no cost to entering into a forward contract. Options, on the other hand, involve the payment of premiums. In this case, Joe has to pay for a call option and receives the value of a put option. 30
Synthetic Forward Let C and P denote the premium of a call and put option, respectively. Then Joe has to pay C P to create the synthetic forward. If C P < 0 then Joe receives some money up front. That is, if the put option is worth more than the call option, then the synthetic forward is better than the forward contract itself due to the premium he collected when the portfolio is formed. 31
Synthetic Forward If Joe expected to collect USD1,000,000 in 90 days, then he needs to buy a put a write call to form a synthetic forward. 32
Option Pricing and Valuation The value of an option can be divided in two components Total Value (Premium) = Intrinsic Value + Time Value. 33
Option Pricing and Valuation Consider a call option with a premium of $0.033/ and a strike price of $1.70/. The premium is calculated from the following: Present spot rate: $1.70/. Time to maturity: 90 days. Forward rate on 90-day contracts: $1.70/. USD interest rate: 8.00% per annum. British pound interest rate: 8:00% per annum. Standard deviation of daily spot price movement: 10.00% per annum. 34
Option Pricing and Valuation The intrinsic value of an option is its value if exercised immediately, i.e. the spot exchange rate minus the strike price when the option is in-the-money. When out-the-money, the option price is zero. The time value of an option arises from the fact that the spot rate can potentially rise above the spot price. Note that the time value of an option is symmetric, as it is based on an expected distribution of possible outcomes around the forward rate that is also symmetric. 35
Option Pricing and Valuation Intrinsic, time and total value of the 90-Day Call Option on British pounds (in Cents per Pounds, Except for the Spot Rate) Spot ($/ ) 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 Intrinsic value 0.00 0.00 0.00 0.00 0.00 1.00 2.00 3.00 4.00 Time value 1.67 2.01 2.39 2.82 3.30 2.82 2.39 2.01 1.67 Total value 1.67 2.01 2.39 2.82 3.30 3.82 4.39 5.01 5.67 36
Currency Options Pricing Sensitivity The value of an option depends on: The forward rate; The spot rate; Its time to maturity; The volatility of the spot rate; The interest rate differential; Its strike price. 37
Currency Options Pricing Sensitivity Forward Rate Sensitivity Foreign currency options are priced around the forward rate. Let F 90 denote the 90-day forward rate in $/, let S denote the current spot rate in $/, and let i $ and i denote the annual interest rate in dollars and pounds, respectively. The absence of (risk-free) arbitrage opportunities means that saving in $ yields the same return as saving in. 38
Currency Options Pricing Sensitivity Forward Rate Sensitivity That is, and thus 1 + i $ 90 360 = 1 ( S 1 + i 90 ) F 90. 360 F 90 = S 1 + i $/4 1 + i /4. 39
Currency Options Pricing Sensitivity Spot Rate Sensitivity (delta) delta = Premium Spot Rate Strike ($/ ) Spot ($/ ) Premium Intrinsic Time Delta 1.70 1.75 6.37 5.00 1.37.71 1.70 1.70 3.30 0.00 3.30.50 1.70 1.65 1.37 0.00 1.37.28 40
Currency Options Pricing Sensitivity Spot Rate Sensitivity (delta) Delta measures the sensitivity of the premium to small changes in the spot rate. That is, it is the slope of the curve in Exhibit 5.8. At S = $1.73/, delta is approximately equal to.0567.0501 1.74 1.73 =.66 41
Currency Options Pricing Sensitivity Spot Rate Sensitivity (delta) The delta of a call option varies between 0 and 1. The more in-the-money a call option is, the closer to 1 its delta is. The delta of a put option varies between 1 and 0. The more in-the-money a put option is, the closer to 1 its delta is. Note that the slope of the intrinsic value of a call option (Exhibit 5.8) is equal to 1. 42
Currency Options Pricing Sensitivity Time to Maturity and Value Deterioration (theta) Option values increase with the length of time until maturity. The expected change in the option premium given a small change in the time to maturity is called theta. theta = Premium Time Option premiums deteriorate at an increasing rate as their time to maturity decreases. 43
Currency Options Pricing Sensitivity Sensitivity to Volatility (lambda) Option volatility is the standard deviation of daily percentage changes in the underlying exchange rate. lambda = Premium Volatility Premiums increase with volatility. 44
Currency Options Pricing Sensitivity Sensitivity to Interest Rates (rho and phi) rho = phi = Premium Domestic Interest Rate > 0 Premium Foreign Interest Rate < 0 45
Prudence in Practice Nicholas Leeson was a trader who reduced the value of the Baring Brothers & Co. Bank from $500 million to $1.60 million by trading futures on the Nikkei 225 index from July 1992 until February 1995. In 1992, Leeson was running the back office for the new Baring Futures Singapore (BFS). He was responsible for the back office accounting and control as well as for executing clients orders. 46
Prudence in Practice Leeson decided to write an exam allowing him to trade futures on the Singapore International Monetary Exchange (SIMEX). He did not need this exam to do his job. He could execute clients trades by passing them to the firm s traders. He then created an error account to hide his unauthorized trades. 47
Prudence in Practice Leeson was trading futures and options on the Nikkei 225, an index of Japanese securities. The Nikkei 225 had reached 40,000 in 1989 but had fallen to around 20,000 by mid-1994. Leeson was convinced the index would not fall below 19,000. He started buying (taking long positions in) Nikkei 225 futures contracts. He would be making money had the Nikkei 225 risen. 48
Prudence in Practice Leeson thought that if the Nikkei 225 does not rise, it would be because interest rates would be rising and thus bond prices would be decreasing. To hedge against the possibility of looses on the futures positions, he sold (took short positions on) Japanese bonds futures contracts. The Nikkei 225 index never went high enough for Lesson to make money and interest rates just kept falling in Japan from 1992 to 1995. Leeson was losing money on all his futures contract. 49
Prudence in Practice The money for the margin calls was obtained by writing call and put options on the same index, the Nikkei 225. By the end of 1993, for instance, Leeson wrote for $35 million of options to cover his losses of $30 million. On January 17, 1995, the earthquake devastated the Japanese city of Kobe and, by January 20, the Nikkei had plummeted below 18,840. Leeson doubled his long positions on the Nikkei futures but the index kept falling. 50
Prudence in Practice In 1995, the Nikkei index was at 18,000 and Leeson was long 55,399 unhedged Nikkei futures. At that time, the losses incurred by Leeson amounted to $1.1 billion. 51