Black-Scholes put and call option pricing
[Call,Put] = blsprice(Price,Strike,Rate,Time,Volatility)
[Call,Put] = blsprice(___,Yield)
Note: Any input argument can be a scalar, vector, or matrix. If a scalar, then that value is used to price all options. If more than one input is a vector or matrix, then the dimensions of those non-scalar inputs must be the same.
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
The S&P 100 index is at 910 and has a volatility of 25% per annum. The risk-free rate of interest is 2% per annum and the index provides a dividend yield of 2.5% per annum. Calculate the value of a three-month European call and put with a strike price of 980.
[Call,Put] = blsprice(910,980,.02,.25,.25,.025)
Call = 19.6863
Put = 90.4683
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
Price— Current price of underlying asset
Current price of the underlying asset, specified as a numeric value.
Strike— Exercise price of the option
Exercise price of the option, specified as a numeric value.
Rate— Annualized continuously compounded risk-free rate of return over life of the option
Annualized continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal number.
Time— Time to expiration of option
Time to expiration of the option, specified as the number of years.
Volatility— Annualized asset price volatility
Annualized asset price volatility (that is, annualized standard deviation of the continuously compounded asset return), specified as a positive decimal number.
Yield— Annualized continuously compounded yield of underlying asset over life of the option
0(default) | decimal
(Optional) Annualized continuously compounded yield of the underlying
asset over the life of the option, specified as a decimal number.
Yield is empty or missing, the default value
Yield could represent the dividend
yield (annual dividend rate expressed as a percentage of the price
of the security) or foreign risk-free interest rate for options written
on stock indices and currencies.
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
Call— Price of a European call option
Price of a European call option, returned as a matrix.
Put— Price of a European put option
Price of a European put option, returned as a matrix.
Hull, John C. Options, Futures, and Other Derivatives. 5th edition, Prentice Hall, 2003.
Luenberger, David G. Investment Science. Oxford University Press, 1998.