blsdelta

Black-Scholes sensitivity to underlying price change

Description

example

[CallDelta,PutDelta] = blsdelta(Price,Strike,Rate,Time,Volatility) 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.

example

[CallDelta,PutDelta] = blsdelta(___,Yield) adds an optional argument for Yield.

Examples

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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

Input Arguments

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Current price of the underlying asset, specified as a numeric value.

Data Types: double

Exercise price of the option, specified as a numeric value.

Data Types: double

Annualized, continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal value.

Data Types: double

Time (in years) to expiration of the option, specified as a numeric value.

Data Types: double

Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), specified as a positive decimal value.

Data Types: double

(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, Yield could represent the dividend yield. For currency options, Yield could be the foreign risk-free interest rate.

Data Types: double

Output Arguments

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Delta of the call option, returned as a numeric value.

Delta of the put option, returned as a numeric.

 Hull, John C. Options, Futures, and Other Derivatives. 5th edition, Prentice Hall, 2003.