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.

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

[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.