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blsdelta

Black-Scholes sensitivity to underlying price change

Syntax

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

Arguments

Price

Current price of the underlying asset.

Strike

Exercise price of the option.

Rate

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

Time

Time to expiration of the option, expressed in years.

Volatility

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

Yield

(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.

Description

[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 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.

Examples

expand all

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

References

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

See Also

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