These graphs show the fit between my method using simple analytics and monte carlo density. We can see that analytic density is quite exact for dt-integral but has some mismatch for dz-integral. I am trying to improve this mismatch. It is a matter of better interpolation. dz-integral is defined as integral of Z(t)^p dz(t), Z(0)=1.0, Vol=.35, T=1.0;In the above graph p=0.5; where dZ(t)=Vol*dz(t)dt-integral is defined as integral of Z(t)^p dt, Z(0)=1.0, Vol=.35, T=1.0;;In the above graph p=0.5; where dZ(t)=Vol*dz(t)I will post more graphs tomorrow for p=-.5, p=4.0; The red analytic graph is cut close to zero to avoid instabilities. The problems with zero will be refined later.Please notice that title of first graph is wrong. It is integral of sqrt(Z(t))dt instead.
Last edited by Amin
on July 11th, 2013, 10:00 pm, edited 1 time in total.