# 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 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.

## 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 ```