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blsimpv

Black-Scholes implied volatility

Syntax

Volatility = blsipmv(Price,Strike,Rate,Time,Value)
Volatility = blsimpv(___,Limit,Yield,Tolerance,Class)

Description

example

Volatility = blsipmv(Price,Strike,Rate,Time,Value) using a Black-Scholes model computes the implied volatility of an underlying asset from the market value of European call and put options.

    Note:   The input arguments Price, Strike, Rate, Time, Value, Yield, and Class can be scalars, vectors, or matrices. If scalars, then that value is used to compute the implied volatility from all options. If more than one of these inputs is a vector or matrix, then the dimensions of all non-scalar inputs must be the same.

    Also, ensure that Rate, Time, and Yield are expressed in consistent units of time.

example

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

Examples

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This example shows how to compute the implied volatility for a European call option trading at $10 with an exercise price of $95 and three months until expiration. Assume that the underlying stock pays no dividend and trades at $100. The risk-free rate is 7.5% per annum. Furthermore, assume that you are interested in implied volatilities no greater than 0.5 (50% per annum). Under these conditions, the following statements all compute an implied volatility of 0.3130, or 31.30% per annum.

Volatility = blsimpv(100, 95, 0.075, 0.25, 10, 0.5);
Volatility = blsimpv(100, 95, 0.075, 0.25, 10, 0.5, 0, [], {'Call'});
Volatility = blsimpv(100, 95, 0.075, 0.25, 10, 0.5, 0, [], true)
Volatility = 0.3130

Input Arguments

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Current price of the underlying asset, specified as a numeric value.

Data Types: double

Exercise price of the 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 option, specified as the number of years.

Data Types: double

Price of a European 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) Annualized continuously compounded yield of the underlying asset over the life of the option, specified as a decimal number. If Yield is empty or missing, the default value is 0.

For example, for options written on stock indices, Yield could represent the dividend yield. For currency options, Yield could be the foreign risk-free interest rate.

    Note:   blsimpv can handle other types of underlies like Futures and Currencies. When pricing Futures (Black model), enter the input argument Yield as:

    Yield = Rate
    When pricing currencies (Garman-Kohlhagen model), enter the input argument Yield as:
    Yield = ForeignRate
    where ForeignRate is the continuously compounded, annualized risk-free interest rate in the foreign country.

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 option prices, returned as a decimal number. If no solution is found, blsimpv returns NaN.

References

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

Luenberger, David G. Investment Science. Oxford University Press, 1998.

Introduced before R2006a

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