I'm trying to better understand the Black and Scholes model; which is a scalar function on (positive reals)^5.
a maplesoft worksheet defines it as
I am trying to understand the parameter vectors (r ,T,K,S,sigma) that give the same values of BS_Price - and particularly whether these form curves, closed curves, surfaces or similar.
Right now, I am not sure how to procede.
I've just put together a procedure that evaluates BS at points in R^5 - and i think i can move forward by using the curry or rcurry functions to get a 5d tensor of the values of BS, that i can start to look for patterns within.
BS_Price := proc (InterestRate, StockPrice, StrikePrice, Duration, Volatility) evalf(subs([r = InterestRate, S = StockPrice, K = StrikePrice, T = Duration, sigma = Volatility], exp(-r*T)*(-(1/2)*erf((1/4)*sqrt(2)*(sigma^2*T-2*r*T+2*ln(K)-2*ln(S))/(sigma*sqrt(T)))+1/2))) end proc
could anyone give me advice on doing this?