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.

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.

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