SPANŽ Risk Manager - Option Pricing Models



Models supported

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:

Calculations in monetary terms

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 process is analogous for calculating theoretical option prices:

 (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.)