Implied volatility for futures options from Black model

`Volatility = blkipmv(Price,Strike,Rate,Time,Value)`

`Volatility = blkimpv(___,Name,Value)`

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

= blkipmv(`Price`

,`Strike`

,`Rate`

,`Time`

,`Value`

)`Class`

name-value
argument is empty or unspecified, the default is a call option

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.

Ensure that `Rate`

and `Time`

are
expressed in consistent units of time.

specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.`Volatility`

= blkimpv(___,`Name,Value`

)

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

[2] Jäckel, Peter. "Let's Be
Rational." *Wilmott Magazine.*, January, 2015 (https://onlinelibrary.wiley.com/doi/pdf/10.1002/wilm.10395).

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