# 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 = ForeignRatewhere `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`. ```

example

## 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.

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### 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%.