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Choosing the Appropriate Currency Option Pricing Model

The most common closed-form solution for valuing currency options is usually attributed to Garman Kohlhagen (1983). This model is equivalent to an appropriately configured version of the generalized Black Scholes model, where the net cost of carry parameter for all models is calculated as



g = net cost of carry.
r = 'domestic' riskless interest rate.
rf = 'foreign' riskless interest rate.

Both the Garman Kohlhagen and generalized Black Scholes models are derived under a fairly restrictive set of assumptions, including:


The stochastic behaviour of the underlying exchange rate is assumed to be well represented by a Geometric Brownian Motion process. In crude terms this means that rates follow a smooth random walk through time, without any 'extreme' price changes or price spikes.


The option can only be exercised at maturity

All of the currency option pricing models supported in Vanilla Options retain the first assumption. Some of the models are, however, designed to deal with options for which the second assumption is relaxed. The following table indicates the option pricing models that are appropriate for each of the various option types supported by this component.

Exercise Style   Appropriate Model
European   GK, GBS, BLACK, BIN, BIN2
American   BAW, BIN, BIN2
Bermudan   BIN2
Where,   GK = Garman Kohlhagen.
    GBS = Generalized Black Scholes.
    BLACK = Black model for futures options.
    BAW = Barone-Adesi Whaley.
    BIN = Binomial Option Pricing Model with constant timesteps.
    BIN2 = Binomial Option Pricing Model with variable timesteps.

Note that while we list all of the pricing models that can be applied to each type of option, some models are more appropriate than others. For example, although both the Garman Kohlhagen model and the binomial option pricing model can be used to value a European currency option, the Garman Kohlhagen model would be preferred in this case. As the binomial model involves a numerical approximation to the 'true' value (given by Garman Kohlhagen), it is slower to compute and less precise than the Garman Kohlhagen model.

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