# blsrho

Black-Scholes sensitivity to interest rate change

## Syntax

```[CallRho, PutRho]= blsrho(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

```[CallRho, PutRho]= blsrho(Price, Strike, Rate, Time, Volatility, Yield)``` returns the call option rho `CallRho`, and the put option rho `PutRho`. Rho is the rate of change in value of derivative securities with respect to interest rates. `blsrho` uses `normcdf`, the normal cumulative distribution function in the Statistics and Machine Learning Toolbox™

 Note:   `blsrho` 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

collapse all

### Find the Black-Scholes Sensitivity (Rho) to Interest-Rate Change

This example shows how to find the Black-Scholes sensitivity, rho, to interest-rate change.

```[CallRho, PutRho] = blsrho(50, 50, 0.12, 0.25, 0.3, 0) ```
```CallRho = 6.6686 PutRho = -5.4619 ```

## References

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