# 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).

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Added a bounty to see if we can get some more answers. – chrisaycock Mar 18 '11 at 4:01
Can you tell us what you intend to do with model? Relevent answers might depend on that. – Zarbouzou Mar 18 '11 at 11:24
As I've told you, I would like to use it for a case study - namely calculate parameters of the model using the data and then calculate a couple of probabilities (like reachability/reach-avoid) using new developed methods and compare theoretical values with values extracted from the data. – Ilya Mar 18 '11 at 14:06
Fur currencies, keep in mind that you don't have complete freedom --- if you specify EUR-USD and USD-JPY dynamics, then the EUR-JPY dynamics are fixed... (If you specify all currencies against some fixed given currency, say XXX-USD for all other currencies XXX you avoid this problem, but there are other annoyances with this approach, this simplest being variation in quoting conventions for various currencies, e.g. EUR-USD vs. USD-JPY.) – SetTheorist Mar 18 '11 at 20:05
@Gortaur Have you had a chance to evaluate the new suggestions? I'd like to award the bounty in the next couple of days. Also, you should consider accepting an answer if one meets your needs. – chrisaycock Mar 22 '11 at 3:06

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).

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Thanks. What about the model which covers only currencies? – Ilya Mar 20 '11 at 11:02
@Gortaur: All of those models are suitable for both currencies and stocks. There are several non autoregressive models that are applicable for stocks, but don't work well for currencies. – glyphard Mar 20 '11 at 14:22

Have you considered Dynamic Liner Models? I don't know enough about currencies or DLMs to give any more guidance, but it may be worth a few minutes of googling to see if you can apply it.

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Thanks, I will. – Ilya Mar 18 '11 at 14:54

ARMA, VAR, VEC. Please, check this out. http://www.amazon.com/Analysis-Financial-Time-Ruey-Tsay/dp/0471415448

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I really don't see the point of downgrading an answer without explaining why. Especialy when there is only one answer and no comment on it yet. – Zarbouzou Mar 18 '11 at 11:22
Here is the comment. These models are not relevant for the modelling currencies. – Ilya Mar 18 '11 at 14:06