Hello!I need just few opinions..What are the arguments for using SDE based models against time series models (like GARCH). I'm interested mostly in option pricing applications.Or maybe there is such post already? Help please!

This is how I see it:A stochastic difference equation is a discrete time series model that can also be used in approximate option pricing. (It is intrinsically approximate, however good the time series model is at describing the historic time series, because the relevant future time steps are not known and have to be simulated.)A stochastic differential equation is assumed to be obtainable by taking the infinitessimal limit of the discrete version and can then sometimes be used to obtain an analytic pricing formula. (But, again, the relationship to the future time series as the limit is taken is speculative -- e.g. assuming constant volatility.)

SDE-based models are looking forward (calibrated to implieds), time series models are looking backward (driving forward by looking backwards in a mirror)

Thanx for the input..I've just read in Cont&Tankov book (Financial modelling with jump processes.) that "...a model may perform well based on the returns on a given time horizon, say delta_1 but fail to do so for another horizon delta_2. Also, most time series models in popular use are not stable under time aggregation: for example, if returns computed at interval delta follow a GARCH(1,1) process, returns computed at interval 2*delta do not in general follow a GARCH process..."Does it look familiar to you? I mean have you had such problems with t-s?