Maximilian Lklweryc
2012-Nov-24 08:20 UTC
[R] How to discretize the Variance Gamma Process for stock price simulation?
Hi, I want to do stock price simulation. First of all, I used the geometric brownian motion. To simulate the values, I used not the closed form solution for the GBM given by: S_t=S_0*exp[(???^2)t+?Wt] but the discrete version, so I can "see" every day realization: S_i+1=??t?S_i+???t?S_i+S_i Now I wanted to do the same with the variance gamma distribution model given by: S_T=S_0*exp((r?q)T+w+z) but the problem is, that with this formula I can only observe the final realizations on time point T. Not the values between. I need a discrete version. Can you tell me which formula I have to use? Or how can I solve this problem? I found several papers, but I could not find a solution for my problem, the most "famous" paper could be the following: Variance-Gamma and Monte Carlo, Michael C. Fu http://www.rhsmith.umd.edu/faculty/mfu/fu_files/Fu07.pdf I have the implementation of the variance gamma process for the final T values from Hull: Options Futures and Other Derivatives 7 ed page 587 the basic steps are (simplified): 1. sample gamma distributed values g 2. sample normal distributed values z with mean theta*g and standard deviation sigma * sqrt(g) 3. put the values in the formula (calculate w before) 4. this gives the final values S_T Thanks a lot for your help