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Black-Scholes sensitivity to underlying price change


[CallDelta, PutDelta] = blsdelta(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.


[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. blsdelta uses normcdf, the normal cumulative distribution function in the Statistics and Machine Learning Toolbox™.

    Note:   blsdelta 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.


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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. 5th edition, Prentice Hall, , 2003.

Introduced before R2006a

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