Documentation

blkimpv

Implied volatility for futures options from Black model

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

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(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

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, 'Limit',0.5);
Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 'Limit',0.5,'Class',{'Call'});
Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 'Limit',0.5,'Class',true);
Volatility = blkimpv(20, 20, 0.09, 4/12, 1.1166, 'Limit',0.5,'Class',true,'Method','jackel2016')
Volatility = 0.2500

Input Arguments

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

Data Types: double

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

Data Types: double

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

Data Types: double

Time to expiration of the futures option, specified as the number of years using a scalar numeric.

Data Types: double

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

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Volatility = blkimpv(Yield,CouponRate,Settle,Maturity,'Method','jackel2016')

Upper bound of the implied volatility search interval, specified as the comma-separated pair consisting of 'Limit' and a positive scalar numeric. If Limit is empty or unspecified, the default is 10, or 1000% per annum.

Note

If you are using Method with a value of 'jackel2016', the Limit argument is ignored.

Data Types: double

Implied volatility termination tolerance, specified as the comma-separated pair consisting of 'Tolerance' and a positive scalar numeric. If empty or missing, the default is 1e-6.

Note

If you are using Method with a value of 'jackel2016', the Tolerance argument is ignored.

Data Types: double

Option class indicating option type (call or put) from which implied volatility is derived, specified as the comma-separated pair consisting of 'Class' and a logical indicator, cell array of character vectors, or string array.

To specify call options, set Class = true or Class = {'call'}. To specify put options, set Class = false or Class = {'put'} or Class = ["put"]. If Class is empty or unspecified, the default is a call option.

Data Types: logical | cell | string

Method for computing implied volatility, specified as the comma-separated pair consisting of 'Method' and a character vector with a value of 'search' or 'jackel2016' or a string with a value of "search" or "jackel2016".

Data Types: char | string

Output Arguments

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

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

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

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