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Implied volatility for futures options from Black model

`Volatility = blkimpv(Price, Strike, Rate, Time, Value, Limit,`

Tolerance, Class)

| Current price of the underlying asset (a futures contract). |

| 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 to expiration of the option, expressed in years. |

| Price of a European futures option from which the implied volatility of the underlying asset is derived. |

| (Optional) Positive scalar representing the upper bound
of the implied volatility search interval. If |

| (Optional) Implied volatility termination tolerance. A positive scalar. Default = 1e-6. |

| (Optional) Option class (call or put) indicating the
option type from which the implied volatility is derived. |

```
Volatility = blkimpv(Price, Strike, Rate, Time, CallPrice,
MaxIterations, Tolerance)
```

computes the implied volatility
of a futures price from the market value of European futures options
using Black's model.

`Volatility`

is the implied volatility of the
underlying asset derived from European futures option prices, expressed
as a decimal number. If no solution is found, `blkimpv`

returns `NaN`

.

Any input argument can be a scalar, vector, or matrix. When a value is a scalar, that value is used to compute the implied volatility of all the options. If more than one input is a vector or matrix, the dimensions of all nonscalar inputs must be identical.

`Rate`

and `Time`

must be
expressed in consistent units of time.

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

Black, Fischer. "The Pricing of Commodity Contracts." *Journal
of Financial Economics.* March 3, 1976, pp. 167–79.

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