blsrho

Black-Scholes sensitivity to interest-rate change

Syntax

[CallRho,PutRho] = blsrho(Price,Strike,Rate,Time,Volatility)

[CallRho,PutRho] = blsrho(___,Yield)

Description

[CallRho,PutRho] = blsrho(Price,Strike,Rate,Time,Volatility) 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™.

In addition, you can use the Financial Instruments Toolbox™ object framework with the BlackScholes (Financial Instruments Toolbox) pricer object to obtain price and rho values for a Vanilla, Barrier, Touch, DoubleTouch, or Binary instrument using a BlackScholes model.

Note

blsrho can also handle an underlying asset such as currencies. 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.

[CallRho,PutRho] = blsrho(___,Yield) adds an optional argument for Yield.

Examples

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

Input Arguments

Price — Current price of underlying asset

numeric

Current price of the underlying asset, specified as a numeric value.

Data Types: double

Strike — Exercise price of option

numeric

Exercise price of the option, specified as a numeric value.

Data Types: double

Rate — Annualized, continuously compounded risk-free rate of return over life of option

positive decimal

Annualized, continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal value.

Data Types: double

Time — Time (in years) to expiration of the option

numeric

Time (in years) to expiration of the option, specified as a numeric value.

Data Types: double

Volatility — Annualized asset price volatility

positive decimal

Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), specified as a positive decimal value.

Data Types: double

Yield — Annualized, continuously compounded yield of the underlying asset over life of option

0 (default) | decimal

(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

CallRho — Call option rho

numeric

Call option rho, returned as a numeric value.

PutRho — Put option rho

numeric

Put option rho, returned as a numeric value.

More About

Rho

A rho sensitivity measures the rate at which the price of an option is expected to change in response to a change in the risk-free interest rate.

Rho is expressed as the amount of money an option's price would gain or lose for a one percentage point (1%) change in the risk-free interest rate. For instance, if a call option has a rho of 0.05, it means that for every one percentage point increase in interest rates, the price of the call option is expected to increase by $0.05.

References

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

Version History

Introduced in R2006a