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Okay, here's what I'm doing: 1) formulate a diffusion model of the stock price of the form dS(t) = Exp{ f(s,t) + dW(t) } + dN(t) ; where S(t) is the stock price, f(s,t) is a predictable process, W(t) is the Wiener process, and N(t) is a certain discrete markov process. Parameters for these functions are estimated, using maximum liklihood estimators when possible, from previous stock price data and fundamentals. Monte Carlo simulations can be used to test the statistical power of a test under a certain stochastic model. These simulations across a large part of the parameter space, as well as analytic work has suggested that diffusion models preform better than regression models. I hope this helps. Oh, and, yes, I'm aware that different distributions have different probability densities. :-) This kind of stuff is what I do for a living (I've published papers in several probability and math journals). :-) |
