Black-Scholes sensitivity to underlying price change
[CallDelta, PutDelta] = blsdelta(Price, Strike, Rate, Time,
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,
[CallDelta, PutDelta] = blsdelta(Price, Strike, Rate,
Time, Volatility, Yield) returns delta, the sensitivity
in option value to change in the underlying asset price. Delta is
also known as the hedge ratio.
normcdf, the normal cumulative distribution
function in the Statistics and Machine Learning Toolbox™.
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
This example shows how to find the Black-Scholes delta sensitivity for an underlying asset price change.
[CallDelta, PutDelta] = blsdelta(50, 50, 0.1, 0.25, 0.3, 0)
CallDelta = 0.5955 PutDelta = -0.4045
Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.