Black-Scholes sensitivity to underlying price change
returns delta, the sensitivity in option value to change in the underlying asset
price. Delta is also known as the hedge ratio.
PutDelta] = blsdelta(
normcdf, the normal cumulative
distribution function in the Statistics and Machine Learning Toolbox™.
In addition, you can use the Financial Instruments Toolbox™ object framework with the
BlackScholes (Financial Instruments Toolbox) pricer object to obtain price and
delta values for a
Binary instrument using a
blsdelta can handle other types of underlies like
Futures and Currencies. When pricing Futures (Black model), enter the input
Yield = Rate
Yield = ForeignRate
ForeignRateis the continuously compounded, annualized risk-free interest rate in the foreign country.
Find the Sensitivity in Option Value to Change in the Underlying Asset Price
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
Price — Current price of underlying asset
Current price of the underlying asset, specified as a numeric value.
Strike — Exercise price of option
Exercise price of the option, specified as a numeric value.
Rate — Annualized, continuously compounded risk-free rate of return over life of option
Annualized, continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal value.
Time — Time (in years) to expiration of the option
Time (in years) to expiration of the option, specified as a numeric value.
Volatility — Annualized asset price volatility
Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), specified as a positive decimal value.
Yield — Annualized, continuously compounded yield of the underlying asset over life of option
0 (default) | decimal
(Optional) Annualized, continuously compounded yield of the underlying
asset over the life of the option, specified as a decimal value. For
example, for options written on stock indices,
could represent the dividend yield. For currency options,
Yield could be the foreign risk-free interest
CallDelta — Delta of call option
Delta of the call option, returned as a numeric value.
PutDelta — Delta of put option
Delta of the put option, returned as a numeric.
 Hull, John C. Options, Futures, and Other Derivatives. 5th edition, Prentice Hall, 2003.
Introduced in R2006a