Black-Scholes sensitivity to interest rate change
[CallRho, PutRho]= blsrho(Price, Strike, Rate, Time, Volatility,
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,
[CallRho, PutRho]= blsrho(Price, Strike, Rate, Time,
Volatility, Yield) returns the call option rho
and the put option rho
PutRho. Rho is the rate
of change in value of derivative securities with respect to interest
the normal cumulative distribution function in the Statistics and Machine Learning Toolbox™
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
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, Prentice Hall, 5th edition, 2003.