blslambda

Black-Scholes elasticity

Syntax

[CallEl,PutEl] = blslambda(Price,Strike,Rate,Time,Volatility)

[CallEl,PutEl] = blslambda(___,Yield)

Description

[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™.

In addition, you can use the Financial Instruments Toolbox™ object framework with the BlackScholes (Financial Instruments Toolbox) pricer object to obtain price and lambda values for a Vanilla, Barrier, Touch, DoubleTouch, or Binary instrument using a BlackScholes model.

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.

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

Examples

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

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

Price — Current price of underlying asset

numeric

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

Data Types: double

Strike — Exercise price of option

numeric

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

Data Types: double

Rate — Annualized, continuously compounded risk-free rate of return over life of option

positive decimal

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

Data Types: double

Time — Time (in years) to expiration of the option

numeric

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

Data Types: double

Volatility — Annualized asset price volatility

positive decimal

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

Data Types: double

Yield — Annualized, continuously compounded yield of the underlying asset over life of option

0 (default) | decimal

(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

CallEl — Call option elasticity

numeric

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

PutEl — Put option elasticity

numeric

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

More About

Lambda

A lambda sensitivity measures the percentage change in an option's price for a 1% change in the price of the underlying asset.

Lambda is a measure of leverage, indicating how much more sensitive an option is to price movements in the underlying asset compared to owning the asset outright. For example, if an option has a lambda of 3, it means that if the underlying asset's price moves by 1%, the option's price is expected to move by 3%.

References

[1] Daigler, R. Advanced Options Trading. McGraw-Hill, 1993.

Version History

Introduced in R2006a