Main Content

# blkprice

Black model for pricing futures options

## Syntax

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

## Description

example

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

collapse all

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

collapse all

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

Data Types: `double`

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

Data Types: `double`

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

Data Types: `double`

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

Data Types: `double`

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

Data Types: `double`

## Output Arguments

collapse all

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

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

## 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