Thanks for asking. Maybe I am making things way too complicated, but this is what I like to do.
Using Black Scholes, or other options pricing models to simulate the behavior of the option price as a function of the various variables. For example in Black Scholes:
C = F(S, K, IV, t, r, d)
C = call premium
F = function, e.g. Black Scholes
S = Underlying price
K = Strike
IV= implied volatility
t = time to expiry
r = risk free rate
d = dividend rate
I want to calculate a time series of C, changing the value of S(t), IV(t) as time unfolds, S(t) can be lognormal or historical or fat tail.., IV can be a constant or follow some empirical skew function... I can use a random number generator and the lognormal function to create S(t) as time unfolds.
Since C is path dependent, to see how the most likely value of C unfolds as a function of time depends on S(t). For this time series calculation, a simple Excel will do. But I need to run enough cases to get the most likely C(t) and therefore a Monte Carlo. In my younger days using FORTRAN to run Monte Carlo, I typically ran ~100,000 cases. Not practical to do that with Excel without a do loop. I can do it with VBA but I don't know how to create functions for the Black Scholes equation within the VBA subroutine.
I thought at first that the most likely C(t) would be to calculate S(t) as if it grows as square root of (IV*t) but could not prove that mathematically, so am resorting to a numerical simulation. Plus, with a numerical simulation, I can input any function for S.
Am I making any sense? If not, please set me straight.
Thanks again.