compute the Rho of a European-style option with given payoff
BlackScholesRho(S0, K, T, sigma, r, d, optiontype)
BlackScholesRho(S0, P, T, sigma, r, d)
algebraic expression; initial (current) value of the underlying asset
algebraic expression; strike price
algebraic expression; time to maturity
algebraic expression; volatility
algebraic expression; continuously compounded risk-free rate
algebraic expression; continuously compounded dividend yield
operator or procedure; payoff function
call or put; option type
The Rho of an option or a portfolio of options is the sensitivity of the option or portfolio to changes in the risk-free rate
The BlackScholesRho command computes the Rho of a European-style option with the specified payoff function.
The parameter S0 is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.
The parameter K specifies the strike price if this is a vanilla put or call option. Any payoff function can be specified using the second calling sequence. In this case the parameter P must be given in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.
The sigma, r, and d parameters are the volatility, the risk-free rate, and the dividend yield of the underlying asset. These parameters can be given in either the algebraic form or the operator form. The parameter d is optional. By default, the dividend yield is taken to be 0.
First you compute the Rho of a European call option with strike price 100, which matures in 1 year. This will define the Rho as a function of the risk-free rate, the dividend yield, and the volatility.
In this example you will use numeric values for the risk-free rate, the dividend yield, and the volatility.
We can also use the generic method in which the option is defined through its payoff function.
Ρ ≔ BlackScholesRho⁡100,K,1,σ,0.05,0.03,'call'
Here are similar examples for the European put option.
In this example, you will compute the Rho of a strangle.
S ≔ BlackScholesRho⁡100,t→piecewise⁡t<50,50−t,t<100,0,t−100,1,σ,r,d
C ≔ BlackScholesRho⁡100,100,1,σ,r,d,'call'
P ≔ BlackScholesRho⁡100,50,1,σ,r,d,'put'
Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.
The Finance[BlackScholesRho] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
Download Help Document
What kind of issue would you like to report? (Optional)