Black model for pricing futures options
[Call, Put] = blkprice(Price, Strike, Rate, Time, Volatility)
Current price of the underlying asset (a futures contract).
Strike or exercise price of the futures option.
Annualized, continuously compounded, risk-free rate of return over the life of the option, expressed as a positive decimal number.
Time until expiration of the option, expressed in years. Must be greater than 0.
Annualized futures price volatility, expressed as a positive decimal number.
[Call, Put] = blkprice(ForwardPrice, Strike, Rate, Time, Volatility) uses Black's model to compute European put and call futures option prices.
Any input argument may be a scalar, vector, or matrix. When a value is a scalar, that value is used to compute the implied volatility from all options. If more than one input is a vector or matrix, the dimensions of all non-scalar inputs must be identical.
Rate, Time, and Volatility must be expressed in consistent units of time.
This example shows how to price European futures options with exercise prices of $20 that expire in four months. Assume that the current underlying futures price is also $20 with a volatility of 25% per annum. The risk-free rate is 9% per annum.
[Call, Put] = blkprice(20, 20, 0.09, 4/12, 0.25)
Call = 1.1166 Put = 1.1166
Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003, pp. 287-288.
Black, Fischer, "The Pricing of Commodity Contracts," Journal of Financial Economics, March 3, 1976, pp. 167-179.