blkprice

Black model for pricing futures options

Syntax

[Call,Put] = blkprice(Price,Strike,Rate,Time,Volatility)

Description

[Call,Put] = blkprice(Price,Strike,Rate,Time,Volatility) computes European put and call futures option prices using Black's model.

Note

Any input argument can be a scalar, vector, or matrix. If a scalar, then that value is used to price all options. If more than one input is a vector or matrix, then the dimensions of those non-scalar inputs must be the same.

Ensure that Rate, Time, and Volatility are expressed in consistent units of time.

Examples

Compute European Put and Call Futures Option Prices Using Black's Model

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

Input Arguments

Price — Current price of underlying asset

numeric

Current price of the underlying asset (that is, a futures contract), specified as a numeric value.

Data Types: double

Strike — Exercise price of the futures option

numeric

Exercise price of the futures option, specified as a numeric value.

Data Types: double

Rate — Annualized continuously compounded risk-free rate of return over life of the option

positive decimal

Annualized continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal number.

Data Types: double

Time — Time to expiration of option

numeric

Time to expiration of the option, specified as the number of years. Time must be greater than 0.

Data Types: double

Volatility — Annualized asset price volatility

positive decimal

Annualized futures price volatility, specified as a positive decimal number.

Data Types: double

Output Arguments

Call — Price of a European call futures option

matrix

Price of a European call futures option, returned as a matrix.

Put — Price of a European put futures option

matrix

Price of a European put futures option, returned as a matrix.

More About

Black Model

The Black model is a financial model used to price options on futures contracts.

Developed by Fischer Black in 1976, this model extends the Black-Scholes option pricing framework to accommodate options on futures rather than stocks. The Black model is particularly useful in situations where the underlying asset is a futures contract, which is common in commodities and interest rate markets.

References

[1] Hull, John C. Options, Futures, and Other Derivatives. 5th edition, Prentice Hall, , 2003, pp. 287–288.

[2] Black, Fischer. “The Pricing of Commodity Contracts.” Journal of Financial Economics. March 3, 1976, pp. 167–79.

Version History

Introduced before R2006a