Heston model

In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process. Basic Heston model The basic Heston model assumes that St, the price of the asset, is determined by a stochastic process, : dS_t = \mu S_t,dt + \sqrt{\nu_t} S_t,dW^S_t, where \nu_t, the instantaneous variance, is given by a Feller square-root or CIR process, : d\nu_t = \kappa(\theta - \nu_t),dt + \xi \sqrt{\nu_t},dW^{\nu}_t, and W^S_t, W^{\nu}_t are Wiener processes (i.e., continuous random walks) with correlation ρ. The model has five parameters:

\nu_0, the initial variance.
\theta, the long variance, or long-run average variance of the price; as t tends to infinity, t

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