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Black-Scholes sensitivity to interest rate change


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



Current price of the underlying asset.


Exercise price of the option.


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


Time to expiration of the option, expressed in years.


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


(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.


[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 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.


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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


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

Introduced before R2006a

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