|
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:
g = r - c
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,
| |
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 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
|
