blslambda

Black-Scholes elasticity

Syntax

[CallEl, PutEl] = blslambda(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

[CallEl, PutEl] = blslambda(Price, Strike, Rate, Time, Volatility, Yield) returns the elasticity of an option. CallEl is the call option elasticity or leverage factor, and PutEl is the put option elasticity or leverage factor. Elasticity (the leverage of an option position) measures the percent change in an option price per one percent change in the underlying asset price. blslambda uses normcdf, the normal cumulative distribution function in the Statistics Toolbox™.

    Note:   blslambda 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

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Find the Black-Scholes Elasticity (Lambda) for an Option

This example shows how to find the Black-Scholes elasticity, or leverage, of an option positon.

[CallEl, PutEl] = blslambda(50, 50, 0.12, 0.25, 0.3)
CallEl =

    8.1274


PutEl =

   -8.6466

References

Daigler, Advanced Options Trading, Chapter 4.

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