# 6. Foreign Currency Options

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1 6. Foreign Currency Options So far, we have studied contracts whose payoffs are contingent on the spot rate (foreign currency forward and foreign currency futures). he payoffs from these instruments are linear in the future spot rate. hat is, if you buy any of these instruments and the underlying exchange rate increases, you gain proportionally, and when the rate decreases, you lose money proportionally. In other words, the payoff of these instruments is symmetric. Foreign currency options, however, are instruments that permit investors to achieve asymmetric or linear payoffs. Options are instruments that are much more flexible for hedging and for speculating. A foreign currency option is a contract giving the option purchaser (the buyer) the right, but not the obligation, to buy or sell a fixed amount of foreign exchange at a fixed price per unit for a specified time period. 6.1 Options Vocabulary Holder: he buyer of an option is called the holder. Writer: he seller of an option is called a writer or a grantor. Call: A call is an option to buy foreign currency. Put: A put is an option to sell foreign currency. Strike Price: he strike price or exercise price is the price at which the foreign currency can be purchased or sold. Premium: he premium or option price is the cost, price, or value of the option. American Option: An American option gives the holder the right to exercise the option at any time between the date of writhing and the expiration or maturity date. European Option: A European option gives the holder the right to exercise the option only at the expiration date. At-the-Money (AM): An option whose exercise price is the same as the spot price of the underlying currency is said to be at-the-money.

5 6.5 A Graphical Analysis of European Options he put call parity is a relation between the value of a forward contract and a portfolio of put and all options. Forward Payoffs: As we have seen, values for forward purchases and sales at expiration are: V V b s = S = F 0, F 0, S hese payoffs have a graphical representation (see payoff chart with short and long positions). Call Options Payoffs: A call option is a contract that gives the holder the right to buy a stated number of units of the underlying asset (currency) at a given price (the strike price). A call option allows you to obtain only the nice part of the forward purchase. Rather than paying X for the foreign currency (as in the forward purchase), you pay no more than X, and possibly less than X. Denoting the strike price by X, we formally state this as follows. On the expiration day, a call option on one unit of foreign currency is worth: C = MAX ( S X,0) It has a simple graphical representation (see payoff chart with short and long positions). A European call option can only be exercised on the expiration day, such that the current market price is based solely on that final payoff. An American call option can be exercised up to the expiration day, which makes its valuation more complicated. For early exercise to be rations, two conditions must be met: he holder will not exercise early if the payoff is not positive he holder will not exercise when the option's market value exceeds its immediate exercise value because, under these circumstances, it would be better to sell the option than to exercise it. Put Options Payoffs: A put option is a contract that gives the holder the right to sell a stated number of units of the underlying asset (currency) at a given price (the strike price).

6 A put option allows you to obtain only the nice part of the forward sale. Rather than getting X for the foreign currency (as in the forward sale), you get no less than X, and possibly more than X. Denoting the strike price by X, we formally state this as follows. On the expiration day, a call option on one unit of foreign currency is worth: P = MAX ( X S,0) It has a simple graphical representation (see payoff charts with short and long positions). A European put option can only be exercised on the expiration day, such that the current market price is based solely on that final payoff. An American put option can be exercised up to the expiration day, which makes its valuation more complicated. For early exercise to be rations, two conditions must be met: he holder will not exercise early if the payoff is not positive he holder will not exercise when the option's market value exceeds its immediate exercise value because, under these circumstances, it would be better to sell the option than to exercise it. Put Call Parity: A summary comparison of the forward payoff and the put and call payoffs suggests that it is possible to replicate a forward contract using options. For example, the payoff from a forward sale is identical to the payoffs from buying a put and selling a call, when the forward sale is executed at a price equal to the option portfolio's strike price: P C = X S = F0, S Since the future payoffs are the same, the law of one price suggests that the present values of the option portfolio and the forward sale must be the same also. From the equivalence at time, it follows that there must also be equivalence in terms of present values or current values in equilibrium. hat is, the current market value of the option portfolio must be equal to the market value of the forward contract (F=X): P C t t = X F 1 + r t, t, his relationship is called the Put Call Parity (for European currency options).

10 6.7 Option Pricing and Valuation he value of an option is the sum of two components: Option value = Intrinsic value + ime value he Intrinsic value is the financial gain if the option is exercised immediately. It is zero for out-of-the-money and at-the-money options, as no gain can be derived from exercising the option. It becomes positive for in-the-money options. he ime value of an option exists because the price of the underlying currency, the spot rate, can potentially move further in the money between the present time and the option's expiration date. An investor will pay something for an out-of-the-money option on the chance that the spot rate will move far enough before maturity to move the option in the money. Consequently, the price of an option is always somewhat greater than its intrinsic value prior to maturity. On the date of maturity, an option will have a value equal to its intrinsic value (zero time remaining means zero time value). Note that for identical maturity and strike price, an American option is more valuable, since it can be exercised up to maturity while the European option can only be exercised at maturity. he pricing of a currency option combines 6 elements. he premium is based on 1. he forward rate 2. he current spot rate 3. he time to maturity 4. he volatility of the underlying asset 5. he home and foreign interest rates 6. he strike price If currency options are to be used effectively, the individual trader needs to know how option values premium react to their various components. 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. Regardless of the specific strike rate, the forward rate is central to valuation. Spot Rate Sensitivity (Delta): As long as the option has time remaining before expiration, the option will possess this time value element. his characteristic is one of the primary reasons why an American option, which can be exercised on any day up to and including the expiration date, is

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