I am relatively new to Mathematica, and have been using it for a few finance applications recently.
One particular thing I have been trying to replicate within Mathematica is a few option pricing formulas (namely the black-scholes option pricing formula) for European Options.
I have a formula i.e.
c = S* Exp(-D*T) * N(d1) - X *Exp(-r*T) * N(d2)
where N is a cumulative normal distribution function of d1, S = stock price, X = strike price, D = dividend yield, T = time, and r = interest rate.
d1 and d2 are each given by their respective formulae:
d1 = (ln(S/X) + (r - D * 0.5 * V^2) * T)/V * SQRT(T)
d2 = d1 - V*SQRT(T)
Although those are not important for what i'm trying to find out here.
I want to know if it is possible to plot a 3 dimension graph of c (the option price) on the y axis, and for example, D on the x asis and V on the z axis.
Where c = f(S, X, r, D, T, V)
I'm trying to show how changes in two of the variables will affect the value of c.
Any suggestions as to where to begin? I'm assuming that it should be a Parametric3dPlot function or something similar.
I hope this makes some sense. Many thanks in advance.