April 29th, 2013, 2:13 pm
Try to do it yourself (there are many related articles) and post questions when you get stuck. The Heston char. function has a simple form phi(T,v,x,z) = E[exp(i z X(T)) | X(0)=x, V(0)=v ] = exp{A(T) + B(T) v} (supressing some dependencies) and this still holds when the parameters are piecewise constant (or general time-varying). It is a matter of solving some ODE's for A(T) and B(T) recursively along the piecewise stretches.These ODE's are found by substitution of the soln form in the Kolmogorov backward eqn.If those ODE's can't' be solved analytically, something like Mathematica could certainly solve them easilynumerically and you would then have it.
Last edited by
Alan on April 28th, 2013, 10:00 pm, edited 1 time in total.