How to Use Pricing Models for Foreign Exchange Options
Caplan, David, Modern Trader
How to use pricing models for foreign exchange options
The increasing volume of international trade and the quick adjustment of prices means many financial institutions are exposed to greater risks from currency fluctuations than before.
The three main markets for managing these currency risks are options, futures and swaps. Because of their pricing mechanisms, option pricing tools and their related derivatives are the most complicated of the three market alternatives.
Among the many models used in options pricing, the two most popular continue to be the Black-Scholes model, based on the assumption that the price of the underlying commodity has a (continuous) lognormal distribution, and the Cox-Ross-Rubinstein model, based on the assumption that the price of the underlying commodity has a multiplicative binomial distribution.
The two approaches are quite different regarding the above distributions, but they are similar in other respects. Both assume constant volatility and interest rates over the lifetime of the option.
In foreign exchange, a well-known arbitrage condition called interest rate parity is extremely important in pricing options. The interest rate parity implies that the domestic interest rate (plus 1) divided by the foreign interest rate (plus 1) should equal the ratio of the forward over the spot exchange rates. Some traders price options based on the forward price, even though they trade options on the spot rates. This is done to examine the price differential of a spot option vs. a forward option and to look for arbitrage opportunities while making a market.
When the underlying price distribution is believed to be continuous--that is, price changes are moderate and the distribution resembles the lognormal -- the proper model to price European options on the spot rate is that of Garman and Kohlhagen, which is based on the Black-Scholes model.
The pricing formulas will yield good results for options with long maturities. The reason: The longer the maturity of the option, the more likely the distribution of the underlying price will approach the lognormal.
If you choose to evaluate an option on a forward price, the proper model to use is the 1976 Black model. When the underlying price distribution is believed to be discreet -- the price jumps up or down rather than moving smoothly -- the binomial distribution can be applied, and the European pricing model should be used.
The appropriate risk-free interest rate in the model should be the ratio of the domestic rate (plus 1) to the foreign rate (plus 1).
An adjustment of each of the above models can be done to price American-type options. For the lognormal distribution, the adjustment is based on the option's early exercise value.
Using the binomial distribution to price an American option implies that you lose the closed-form formula and the model becomes a process of evaluation. At each node of the binomial pricing tree, the option price should be the greater of the intrinsic value and the two dates' binomial value. …