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 =
[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility,
Yield) computes European put and call option prices using
a Black-Scholes model.
Any input argument can 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.
Yield must be expressed in consistent units
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
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
Price an FX option on buying GBP with USD.
S = 1.6; % spot exchange rate X = 1.6; % strike T = .3333; r_d = .08; % USD interest rate r_f = .11; % GBP interest rate sigma = .2; Price = blsprice(S,X,r_d,T,sigma,r_f)
Price = 0.0639
Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.
Luenberger, David G., Investment Science, Oxford University Press, 1998.