The SPAN Risk Manager currently supports a variety of option pricing models, and is built so that new models can easily be added.
Each pricing model is assigned an identifier - for example, BS for the Black-Scholes model.
The descriptions below identify options as being either European (meaning exercise is only allowed at expiration) or American (meaning exercise is allowed at any time up to and including expiration.)
The models utilize three interest-rate values:
The cost of carry is defined as the risk-free rate less the dividend yield.
The following pricing models are supported:
The price of an option is not necessarily quoted in the same terms as the price of its underlying. Nor is the option necessarily defined as being only one one of its underlying instrument. And the currency of denomination of the option may not be the same as the currency for its underlying.
When running option pricing models in the forward direction (to calculate option prices and greeks) or in the reverse direction (to calculate implied volatilities), it is necessary always to ensure that the option value, underlying value, and exercise value are correctly specified.
To do so, the SPAN Risk Manager always does option pricing calculations in monetary terms. For example, to calculate an option implied volatility:
The option's monetary value in its settlement currency is determined.
The exact monetary value of the underlying of the option is determined and is expressed in the settlement currency of the option.
Similarly, the exercise value for the option is determined, likewise in the settlement currency of the option.
It is these monetary values which are fed to the option pricing model in order to determine the implied volatility.
The process is analogous for calculating theoretical option prices:
The true underlying value and the exercise value are calculated in the option's settlement currency.
These are fed to the option pricing model to determine the option's theoretical monetary value.
The option monetary value is divided by the contract value factor for the option to calculate the theoretical price.
The theoretical price is then rounded to the normal precision for quoting prices for that option. For example, if prices for a particular option product family are quoted to two decimal places, then the theoretical price is rounded to the nearest 0.01.
The option theoretical value is then recalculated by multiplying the rounded theoretical price by its contract value factor.
(Given the normal conventions used for assigning the precision of option prices and the contract value factors, this last step ensures the theoretical value is always exactly equal to the product of the price times the contract value factor.)