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blkimpv

Implied volatility for futures options from Black model

Syntax

Volatility = blkipmv(Price,Strike,Rate,Time,Value)
Volatility = blkimpv(___,Limit,Tolerance,Class)

Description

example

Volatility = blkipmv(Price,Strike,Rate,Time,Value) computes the implied volatility of a futures price from the market value of European futures options using Black's model.

    Note:   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.

example

Volatility = blkimpv(___,Limit,Tolerance,Class) adds optional arguments for Limit, Tolerance, and Class.

Examples

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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

Input Arguments

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Current price of the underlying asset (that is, a futures contract), specified as a numeric value.

Data Types: double

Exercise price of the futures option, specified as a numeric value.

Data Types: double

Annualized continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal number.

Data Types: double

Time to expiration of the futures option, specified as the number of years.

Data Types: double

Price of a European futures option from which the implied volatility of the underlying asset is derived, specified as a numeric.

Data Types: double

(Optional) Upper bound of the implied volatility search interval, specified as a positive scalar numeric. If Limit is empty or unspecified, the default is 10, or 1000% per annum.

Data Types: double

(Optional) Implied volatility termination tolerance, specified as a positive scalar numeric. If empty or missing, the default is 1e-6.

Data Types: double

(Optional) Option class indicating option type (call or put) from which implied volatility is derived, specified as a logical indicator or a cell array of character vectors.

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.

Data Types: logical | cell

Output Arguments

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Implied volatility of the underlying asset derived from European futures option prices, returned as a decimal number. If no solution is found, blkimpv returns NaN.

References

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.

Introduced before R2006a

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