Q:

Discrete-time model: stock dynamics

I am working in the area of probability theory and for a case study I would like to make some calculations in finance. Since I am developing theory for the discrete time, I am interested in models for the stock price in the discrete time. As I remember GARCH is a good one. Could you advise me something else?
It will be nice if you can tell me which model also can be used for the currency markets (since they are quite faster than the stock markets I think there should another relevant models).

A:

This link is to a book that covers this exact question:
http://onlinelibrary.wiley.com/doi/10.1002/9783527610006.ch9/summary
Summary:  the models that map to both stock markets and currency markets are those that have an autoregressive feature (curreny markets commonly exhibit this feature, limiting the choice of models that apply to both currencies and stocks => *ARCH).  

