Heston model

In finance, the Heston model, named after Steven Heston, is a mathematical model describing 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. In finance, the Heston model, named after Steven Heston, is a mathematical model describing 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. The basic Heston model assumes that St, the price of the asset, is determined by a stochastic process: where ν t {displaystyle u _{t}} , the instantaneous variance, is a CIR process: and W t S , W t ν {displaystyle W_{t}^{S},W_{t}^{ u }} are Wiener processes (i.e., random walks) with correlation ρ, or equivalently, with covariance ρ dt.