# blsdelta

Black-Scholes sensitivity to underlying price change

## Syntax

```[CallDelta, PutDelta] = blsdelta(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

```[CallDelta, PutDelta] = blsdelta(Price, Strike, Rate, Time, Volatility, Yield)``` 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 = ForeignRate`where `ForeignRate` is the continuously compounded, annualized risk free interest rate in the foreign country.

## Examples

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### Find the Sensitivity in Option Value to Change in the Underlying Asset Price

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 ```

## References

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