# blkprice

Black model for pricing futures options

## Syntax

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

## Arguments

 `Price` Current price of the underlying asset (a futures contract). `Strike` Strike or exercise price of the futures option. `Rate` Annualized, continuously compounded, risk-free rate of return over the life of the option, expressed as a positive decimal number. `Time` Time until expiration of the option, expressed in years. Must be greater than 0. `Volatility` Annualized futures price volatility, expressed as a positive decimal number.

## Description

```[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.

## Examples

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### 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 ```

## References

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.