Financial Toolbox

blkimpv

www.kxcad.net Home > CAE Software Index > MATLAB Index >

Implied volatility for futures options from Black's model

Syntax

Volatility = blsimpv(Price, Strike, Rate, Time, Value, Limit, ...     
Tolerance, Class)

Arguments

`Price`	Current price of the underlying asset (a futures contract).
`Strike`	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 to expiration of the option, expressed in years.
`Value`	Price of a European futures option from which the implied volatility of the underlying asset is derived.
`Limit`	(Optional) Positive scalar representing the upper bound of the implied volatility search interval. If `Limit` is empty or unspecified, the default = 10, or 1000% per annum.
`Tolerance`	(Optional) Implied volatility termination tolerance. A positive scalar. Default = 1e-6.
`Class`	(Optional) Option class (call or put) indicating the option type from which the implied volatility is derived. May be either a logical indicator or a cell array of characters. To specify call options, set `Class` `= true` or `Class = {'call'}`; to specify put options, set `Class = false` or `Class = {'put'}`. If `Class` is empty or unspecified, the default is a call option.

Description

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 may 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.

Examples

Consider a European call futures option that expires in four months, trading at $1.1166, with an exercise price of $20. Assume that the current underlying futures price is also $20 and that the risk-free rate is 9% per annum. Furthermore, assume that you are interested in implied volatilities no greater than 0.5 (50% per annum). Under these conditions, the following commands all return an implied volatility of 0.25, or 25% per annum:

Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 0.5)
Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 0.5, [], 
{'Call'})
Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 0.5, [], true)

References

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