This is probably a silly question, but what is the reason that the process for "business time" in the variance gamma model is gamma process, and are there alternative processes that could also be used?

You need an increasing Lévy process as subordinator ("business time") in order to get another Lévy process from a Brownian Motion. Another well-known example is inverse-Gaussian as business time, which gives you Normal inverse Gaussian (NIG).

QuoteOriginally posted by: MosiYou need an increasing Lévy process as subordinator ("business time") in order to get another Lévy process from a Brownian Motion. Another well-known example is inverse-Gaussian as business time, which gives you Normal inverse Gaussian (NIG).I'm curious though, why a gamma process? Is the gamma function unique for this use, or are there any other functions which are usable for this purpose?

have a look at cont and tankovthe gamma process is chosen for its convenience

QuoteOriginally posted by: mjhave a look at cont and tankovthe gamma process is chosen for its convenienceThanks. Cont and Tankov is a *really* good book, and the introduction has a good discussion of basic probability theory that is good even outside of Levy processes.Right now, I'm working on is to look at the general principles that underline subordinators in Levy processes. One thing that is interesting is that the implied volatilities of Shanghai warrants at different strikes are linear functions of each other, and I'm trying to figure out what that means and if the coefficents of the regression mean anything. The other thing is that if I take a short fragment of the time series and graph implied vol versus moneyness, I get a fragment of a smile. If I graph the whole time series, then I get a scatter plot, but I'm 80% sure that this is because the volatility smile is changing over time. I'll try graphing against things other than moneyness to see if I get a better fit. Also as soon as I have a few spare cycles, I'd like to do the analysis that Carr-Wu proposed for short duration options to see if this will give me some insight as to the underlying process.I'm trying to get out one paper or conference talk out a year. Right now my plan is to have the second paper be focused on Shanghai warrants and target a journal that specializes in Asian/emerging markets, and maybe a paper next year if I find something more general. Also, as far as I can tell, nothing I am doing is useful for trading, which has its bad points but some good ones (i.e. because there isn't money to be made, there is much less competition.)