Documentation

# blsdelta

Black-Scholes sensitivity to underlying price change

## Syntax

``[CallDelta,PutDelta] = blsdelta(Price,Strike,Rate,Time,Volatility)``
``[CallDelta,PutDelta] = blsdelta(___,Yield)``

## Description

example

````[CallDelta,PutDelta] = blsdelta(Price,Strike,Rate,Time,Volatility)` returns delta, the sensitivity in option value to change in the underlying asset price. Delta is also known as the hedge ratio. `blsdelta` uses `normcdf`, the normal cumulative distribution function in the Statistics and Machine Learning Toolbox™. Note`blsdelta` 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

````[CallDelta,PutDelta] = blsdelta(___,Yield)` adds an optional argument for `Yield`. ```

## Examples

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This example shows how to find the Black-Scholes delta sensitivity for an underlying asset price change.

`[CallDelta, PutDelta] = blsdelta(50, 50, 0.1, 0.25, 0.3, 0)`
```CallDelta = 0.5955 ```
```PutDelta = -0.4045 ```

## 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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Delta of the call option, returned as a numeric value.

Delta of the put option, returned as a numeric.

 Hull, John C. Options, Futures, and Other Derivatives. 5th edition, Prentice Hall, 2003.