blsprice

Black-Scholes put and call option pricing

Syntax

[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility, Yield)

Arguments

Price

Current price of the underlying asset.

Strike

Exercise price of the 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.

Volatility

Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number.

Yield

(Optional) Annualized, continuously compounded yield of the underlying asset over the life of the option, expressed as a decimal number. (Default = 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.

Description

[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility, Yield) computes European put and call option prices using a Black-Scholes model.

Any input argument may be a scalar, vector, or matrix. When a value is a scalar, that value is used to price all the options. If more than one input is a vector or matrix, the dimensions of all non-scalar inputs must be identical.

Rate, Time, Volatility, and Yield must be expressed in consistent units of time.

    Note:   blsprice 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.

Examples

expand all

Compute European Put and Call Option Prices Using a Black-Scholes Model

This example shows how to price European stock options that expire in three months with an exercise price of $95. Assume that the underlying stock pays no dividend, trades at $100, and has a volatility of 50% per annum. The risk-free rate is 10% per annum.

[Call, Put] = blsprice(100, 95, 0.1, 0.25, 0.5)
Call =

   13.6953


Put =

    6.3497

References

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

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

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