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A mathematical model tracking the occurrence, at each moment after the initial time, of a random phenomenon. Brownian motion, often used to describe security price changes, is a stochastic process. In finance, stochastic processes are a mechanism for describing future prices or rates based on a combination of spot rates or prices and a random variable. Developers of option models attempt to select the random variable-generating process that best matches the empirical pattern. A calculus of stochastic processes forms the basis of many option valuation models. Also called Diffusion Process. See also Brownian Motion, Martingale.
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