# blslambda

Black-Scholes elasticity

## Description

example

[CallEl,PutEl] = blslambda(Price,Strike,Rate,Time,Volatility) 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 1 percent change in the underlying asset price. blslambda uses normcdf, the normal cumulative distribution function in the Statistics and Machine Learning 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.

example

[CallEl,PutEl] = blslambda(___,Yield) adds an optional argument for Yield.

## Examples

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

[CallEl, PutEl] = blslambda(50, 50, 0.12, 0.25, 0.3)
CallEl = 8.1274
PutEl = -8.6466

## 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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Call option elasticity or leverage factor, returned as a numeric value.

Put option elasticity or leverage factor, returned as a numeric value.

## Version History

Introduced before R2006a