[R] How to discretize the Variance Gamma Process for stock price simulation?

[Maximilian Lklweryc]

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[(μ−σ^2)t+σWt]

but the discrete version, so I can "see" every day realization:

S_i+1=μΔt∗S_i+σφΔt∗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