blkimpv

Implied volatility for futures options from Black model

Syntax

Volatility = blkimpv(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

expand all

Find Implied Volatility for Futures Options from Black's Model

This example shows how to find the implied volatility for a European call futures option that expires in four months, trades at $1.1166, and has 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)
Volatility =

    0.2500

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. 167-79.

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