Black-Scholes put and call option pricing
[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility, Yield)
Current price of the underlying asset.
Exercise price of the option.
Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number.
Time to expiration of the option, expressed in years.
Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number.
(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.
[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.
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
Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.
Luenberger, David G., Investment Science, Oxford University Press, 1998.