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Choosing the Appropriate Commodity Option Pricing Model

Options written on most commodities can be approximated using virtually the same collection of models that are used to value currency options. In the case of commodity options, the net cost of carry parameter for each of the various models is defined as:

Equation Template

Where,

g = net cost of carry.

 

r = riskless interest rate.

 

c = net convenience yield from the underlying commodity.

 

 

All of the supported models are derived under a fairly restrictive set of assumptions, including:

 

1.

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

 

2.

The option can only be exercised at maturity.

 

 

 

All of the currency option pricing models supported in Vanilla Options retain the first assumption, and this may not be appropriate for many commodities. Commodity prices often exhibit significant seasonality, mean reversion, or transitory volatility spikes. Because the standard GBM process does not incorporate any of these factors, the option prices generated by the supported models should be treated as a first approximation only.

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

GBS, BLACK, BIN, BIN2

 

American

BAW, BIN, BIN2

 

Bermudan

BIN2

 

 

 

 

Where,

GBS = Generalized Black Scholes.

 

BLACK = Black model for pricing futures.

 

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 Generalized Black Scholes model and the binomial option pricing model can be used to value a European currency option, the Generalized Black Scholes model would be preferred in this case. As the binomial model involves a numerical approximation to the 'true' value (given by the Generalized Black Scholes model), it is slower to compute and less precise than the Generalized Black Scholes model.

 

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