A foreign exchange or currency option contract gives the buyer the right, but not the obligation, to buy (or sell) a specified amount of one currency for another at a specified price on (in some cases, on or before) a specified date.
5. OVER-THE-COUNTER FOREIGN CURRENCY OPTIONS
A foreign exchange or currency option contract gives the buyer the right, but not the obligation, to buy (or sell) a specified amount of one currency for another at a specified price on (in some cases, on or before) a specified date. Options are unique in that the right to execute will be exercised only if it is in the holder’s interest to do so. That differs from a forward contract, in which the parties are obligated to execute the transaction on the maturity date, and it differs from a futures contract, in which the parties are obligated, in principle to transact at maturity, but that obligation easily can be—and normally is— bought out and liquidated before the maturity or delivery date.
A call option is the right, but not the obligation, to buy the underlying currency, and a put option is the right, but not the obligation, to sell the underlying currency.All currency option trades involve two sides—the purchase of one currency and the sale of another—so that a put to sell pounds sterling for dollars at a certain price is also a call to buy dollars for pounds sterling at that price. The purchased currency is the call side of the trade, and the sold currency is the put side of the trade. The party who purchases the option is the holder or buyer, and the party who creates the option is the seller or writer. The price at which the underlying currency may be bought or sold is the exercise, or strike, price. The option premium is the price of the option that the buyer pays to the writer. In exchange for paying the option premium up front, the buyer gains insurance against adverse movements in the underlying spot exchange rate while retaining the opportunity to benefit from favorable movements. The option writer, on the other hand, is exposed to unbounded risk—although the writer can (and typically does) seek to protect himself through hedging or offsetting transactions.
In general, options are written either “European style,” which may be exercised only on the expiration date, or “American style,” which may be exercised at any time prior to, and including, the expiration date. The American option is at least as valuable as the European option, since it provides the buyer with more opportunities, but is analytically more complex. American calls on the higher interest rate currency are likely to be more valuable than the equivalent European option. The bulk of trading in the OTC interbank market consists of European options, while American options are standard on some of the exchanges.
The option is one of the most basic financial instruments. All derivatives, including the
various derivative financial products developed in recent years—the many forms of forwards, futures, swaps, and options—are based either on forwards or on options; and forwards and options, notwithstanding their differences, are related to each other. A forward can be created synthetically from a combination of European options: Buying a call option and selling a put option (long a call, short a put) on a currency with strike prices at the forward rate provides the same risk position as buying a forward contract on that currency. At expiration, the payoff profiles of the forward and the synthetic forward made up of the two options would be the same: The holder would receive the same payoff whether he held the forward or the combination of two options.
As a financial instrument, the option has a long history.But foreign exchange options trading first began to flourish in the 1980s, fostered by an international environment of fluctuating exchange rates, volatile markets, deregulation, and extensive financial innovation. The trading of currency options was initiated in U.S.commodity exchanges
and subsequently was introduced into the over-the-counter market. However, options still account for only a small share of total foreign exchange trading.
An over-the-counter foreign exchange option is a bilateral contract between two parties. In contrast to the exchange-traded options market (described later), in the OTC market, no clearinghouse stands between the two parties, and there is no regulatory body stablishing trading rules.
Also, in contrast to the exchange-traded options market, which trades in standardized
contracts and amounts, for a limited number of currency pairs, and for selected maturity dates, an OTC option can be tailored to meet the special needs of an institutional investor for particular features to satisfy its investment and hedging objectives. But while OTC options contracts can be customized, a very large share of the OTC market consists of generic, or “plain vanilla,” options written for major currencies in standard amounts and for even dates.
OTC options are typically written for much larger amounts than exchange-traded
options—an average OTC option is $30-$40 million equivalent—and a much broader
range of currencies is covered. The volume of OTC options is far greater than that of
exchange-traded options; indeed, the OTC market accounts for about four-fifths of the
total foreign exchange options traded in the United States.
The two options markets, OTC and exchangetraded, are competitors to some extent, but they also complement each other. Traders use both markets in determining the movement of prices, and are alert to any arbitrage opportunities that may develop between the two markets. Dealers in the OTC market may buy and sell options on the
organized exchanges as part of the management of their own OTC positions,hedging or laying off part of an outstanding position in an exchange market.
- The Pricing of Currency Options
It is relatively easy to determine the value of a European option at its expiration. The value of a European option at expiration is its intrinsic value—the absolute amount by which the strike price of the option is more advantageous to the
holder that the spot exchange rate. If at expiration the strike price is more advantageous than the spot rate of the underlying, the option is “in the
money”; if the difference between the strike price and the spot rate is zero, the position is “at the money”; if the strike price is less advantageous than the spot rate, the option is “out of the money.”
Determining the price of an option prior to expiration, on the other hand, is much more
difficult. Before expiration, the total value of an option is based, not only on its intrinsic value (reflecting the difference between the strike price and the then current exchange rate), but also on what is called its time value, which is the additional value that the market places on the option, reflecting the time remaining to maturity, the forecast volatility of the exchange rate, and other factors.
Time value is not linear. A one-year option is not valued at twice the value of a six-month option. An “at-the-money” option has greater time value than an “in-the-money” or “out-ofthe-money” option. Accordingly, options—unlike forwards and futures—have convexity; that is, the change in the value of an option for a given change in the price of the underlying asset does not remain constant. This makes pricing options much more complex than pricing other foreign exchange instruments.
A major advance in the general theory of options pricing was introduced by Professors
Black and Scholes in 1973. Their work, which was subsequently adapted for foreign
exchange options, showed that under certain restrictive assumptions, the value of a
European option on an underlying currency depends on six factors: 1) the spot exchange rate; 2) the interest rate on the base (or underlying) currency; 3) the interest rate on the terms currency; 4) the strike price at which the option can be exercised; 5) the time to expiration; and 6) the volatility of the exchange rate.
Volatility, a statistical measure of the tendency of a market price—in this case, the spot exchange rate—to vary over time, is the only one of these variables that is not known in advance, and is critically important in valuing and pricing options. Volatility is the annualized percentage change in an exchange rate, in terms of standard deviation (which is the most widely used statistical measurement of variation about a mean). The greater the forecast volatility, the greater the expected future movement potential in the exchange rate during the life of the option—i.e., the higher the likelihood the option will move “in-the-money,” and so, the greater the value (and the cost) of the option, be it a put or a call. (With zero volatility, the option should cost nothing.)
If the one-year forward dollar-Swiss franc exchange rate is CHF 1.6000 = $1, and the
volatility of a one-year European option price is forecast at 10 percent, there is implied the expectation, with a 68 percent probability, that one year hence, the exchange rate will be within CHF 1.6000 per dollar plus or minus 10 percent—that is, between CHF 1.4400 and CHF 1.7600 per dollar.
There are different measurements of volatility:
- Historical volatility is the actual volatility, or variance, of an exchange rate that occurred during some defined past time frame. This can be used as an indication or guide to future movements in the exchange rate.
- Future volatility is the expected variance in the exchange rate over the life of the option, and must be forecast.
- Implied volatility is the variance in an exchange rate that is implied by or built into
the present market price of an option—thus, it is the market’s current estimate of future movement potential as determined by supply and demand for the option in the market.
Implied volatility is a critical factor in options pricing. In trading options in the OTC interbank market, dealers express their quotes and execute their deals in terms of implied volatility. It is the metric, or measuring rod—dealers think and trade in terms of implied volatilities and make their predictions in that framework, rather than in terms of options prices expressed in units of a currency (which can change for reasons other than volatility changes—e.g., interest rates). It is easier to compare the prices of different options, or compare changes in market prices of an option over time, by focusing on implied volatility and quoting prices in terms of volatility. (For similar reasons, traders in outright forwards deal in terms of discounts and premiums from spot, rather than in terms of actual forward exchange rates.)
If market quotes and trades are to be made in terms of implied volatilities (or vols),
all traders must use the same concept and conventions for computing volatility, so that they are all speaking the same language. The technique used in the market is to solve the Black-Scholes formula backwards—to take the price of an option in the market as given and calculate the volatility that is implied by that market price. Traders use this Black-Scholes-based computation of implied volatility as a way of communicating and understanding each other, even though they know that it has certain limitations. For example, they know (and take into account) that the technique inherently incorporates into the estimate of “implied volatility” all sources of mispricing, data errors, effects of bid-offer spreads, etc. They also know that the calculation assumes that all of the rigorous assumptions in the Black-Scholes theoretical pricing model apply, whereas in the market in which they are operating in the “real” world, these assumptions may not all apply.
Delta. Another important parameter for assessing options risk, also calculated from
the Black- Scholes equation, is the delta, which measures how much the price of an option changes with a small (e.g., one percent) change in the value of the underlying currency.
Very importantly, the delta is also the hedge ratio, because it tells an option writer or a
holder at any particular moment just how much spot foreign exchange he must be long or short to hedge an option position and eliminate (at least for that moment) the spot position risk.
Thus, if a trader sold a European call option on marks/put option on dollars with the face amount of $10 million, with the strike price set at the forward rate (an “at-the-money forward”), the chances at that moment are about 50-50 that the option will rise in value and at expiration be exercised, or fall in value and at expiration be worthless. If the option at that moment had a delta of 0.50, the trader could hedge, or neutralize, his option risk by taking an opposite spot position (purchase of marks/sale of dollars) equal to 50 percent of the option’s face amount, or $5 million. This is called a “delta hedge.” (If the strike price were “in-the-money,” the delta would be between 0.50 and 1.00; if the strike price were “out-of-the-money,” the delta would be between 0 and 0.50. At expiration, delta ends up either 0 (out-of-the-money and won’t be exercised), or 1.00 (in the money and will be exercised).
Most option traders routinely “delta hedge” each option they purchase or write, buying or
selling in the spot or forward market an amount that will fully hedge their initial exchange rate risk. Subsequently, as the exchange rate moves up or down, the option dealer will consider whether to maintain a neutral hedge by increasing or reducing this initial position in the spot or forward market.
However, the delta, or hedge ratio, whether it starts out at 0.50 or at some other number,
will change continually, not only with each significant change in the exchange rate, but
also with changes in volatility, or changes in interest rates, and, very importantly, delta will change with the passage of time. An option with a longer time to run is more valuable
than an option with a shorter time to run. Thus, new calculations will continually be
required as conditions change, to determine the new delta and the change in spot or
forward foreign exchange position needed to maintain a neutral hedge position.
- Put-Call Parity
“Put-call parity” says that the price of a European put (or call) option can be deduced from the price of a European call (or put) option on the same currency, with the same strike price and expiration.When the strike price is the same as the forward rate (an “at-the-money” forward), the put and the call will be equal in value.When the strike price is not the same as the forward price, the difference between the value of the put and the value of the call will equal the difference in the present values of the two currencies.
Arbitrage assures this result. If the “put-call parity” relationship did not hold, it would pay to create synthetic puts or calls and gain an arbitrage profit. If, for example, an “at-the-money forward” call option were priced in the market at more than (rather than equal to) an “at-the-money forward” put option for a particular currency,a synthetic call option could be created at a cheaper price (by buying a put at the lower price and buying a forward at the market price). Other synthetics can be produced by other combinations (e.g.,buying a
call and selling a forward to produce a synthetic put; buying a call and selling a put to create a synthetic long forward; or selling a call and buying a put to create a synthetic short forward).
The “put-call parity” is very useful to options traders. If, for example, puts for a particular
currency are being traded,but there are no market quotes for the corresponding call, traders can deduce an approximate market price for the corresponding call.
- How Currency Options are Traded
The OTC options market has become a 24-hour market,much like the spot and forward markets, and has developed its own practices and conventions. Virtually all of the major foreign exchange dealer institutions participate as market
makers and traders. They try to stay fully abreast of developments, running global options books that they may pass from one major center to another every eight hours, moving in and out of various positions in different markets as opportunities arise. Some major dealers offer options on large numbers of currency pairs (fifty
or more), and are flexible in tailoring amounts and maturities (from same day to several years ahead). They can provide a wide array of different structures and features to meet customer wishes.
A professional in the OTC interbank options market asking another professional for a quote must specify more parameters than when asking for, say, a spot quote. The currency pair, the type of option, the strike price, the expiration date, and the face amount must be indicated. Dealers can do business with each other directly, by telephone or (increasingly) via electronic dealing system, which makes possible a two-way recorded conversation on a computer screen. Also, they can deal through an OTC (voice) broker. Among these dealers and brokers, quotes are presented in terms of the implied volatility of the option being traded.
As in other foreign exchange markets, a market maker is expected to give both a bid—
the volatility at which he is prepared to buy an option of the specified features—and an offer—the volatility at which he is prepared to sell such an option.
For example, an interbank dealer, Jack from Bank X, might contact a market maker, Jill from Bank Z, identify himself and his institution and ask for a quote:
- Jack: “Three month 50-delta dollar put/yen call on 20 dollars, please.” Jill: “14.50-15.”
- Jack: “Yours at 14.50.” Jill: “Done. I buy European three-month 50-delta dollar put/yen call on 20 dollars.”
After this commitment to the trade, details (“deets”) would then be worked out and agreed upon with respect to the exact expiration date, the precise spot rate, the exact strike price, and option premium. Customarily, in trades between dealers, there would be an offsetting transaction in spot or forward trade, in the opposite direction to the option, to provide both parties with the initial delta hedge.
Note that Jack and Jill specified both currencies—“dollar put/yen call.” In foreign exchange options, since a call allowing you to buy yen for dollars at a certain price is also a put allowing you to sell dollars for yen at that price, it helps to avoid confusion if both formulations are mentioned.
- Options Combinations and Strategies
Combinations of options are used among the professionals for many purposes, including taking directional views on currencies—anticipating that a particular currency will move up or down—as well as taking volatility views on currencies—anticipating that a particular exchange rate will vary by more or by less than the market expects. Among the options combinations that are currently most widely used by traders in the OTC market are the following:
- A straddle consists of one put and one call with the same expiration date, face amount, and strike price. The strike price is usually set at the forward rate—or “at-the-money forward” (ATMF)—where the delta is about 0.50. A long straddle gains if there is higher than forecast volatility, regardless of which of the two currencies in the pair goes up and which goes down—and any potential loss is limited to the cost of the two premiums. By the same token, a short straddle gains if there is less than expected volatility, and the potential gain is limited to the premiums. Thus, a trader buys volatility by buying a straddle, and sells volatility by selling
a straddle. Straddles account for the largest volume of transactions in interbank trading.
- A strangle differs from a straddle in that it consists of a put and a call at different strike prices, both of which are “out-of-the-money,” rather than “at-the-money.” Often the strike prices are set at 0.25 delta. It is a less aggressive position than the straddle—a long strangle costs less to buy, but it requires a higher volatility (relative to market expectations of volatility) to be profitable.
- A risk reversal is a directional play, rather than a volatility play. A dealer exchanges an out-of-themoney (OTM) put for an OTM call (or vice versa) with a counterparty. Since the OTM put and the OTM call will usually be of different values, the dealer pays or receives a premium for making the exchange. The dealer will quote the implied volatility differential at which he is prepared to a make the exchange. If, for example, market expectations that the dollar will fall sharply against the Swiss franc are much greater than market expectations that the dollar will rise sharply
against the Swiss franc, the dealer might quote the price of dollar-swissie risk reversals as follows:
“For a three-month 0.25-delta risk reversal, 0.6 at 1.4 swissie calls over.” That means the dealer is willing to pay a net premium of 0.6 vols (above the current implied ATM volatility) to buy a 0.25-delta OTM Swiss franc call and sell a 0.25-delta OTM Swiss franc put against the dollar, and he wants to earn a net premium of 1.4 vols (above the current implied ATM premium) for the opposite transaction. The holder of a risk reversal who has sold an OTM put and bought an OTM call will gain if the call is exercised, and he will lose if the put is exercised—but unlike the holder of a long straddle or long strangle (where the maximum loss is the
premium paid),on the put he has sold his potential loss is unbounded.
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