The Heston model is a mathematical model used to describe the evolution of financial asset prices, particularly in the context of options pricing. Developed by Steven Heston in 1993, this model is notable for its incorporation of stochastic volatility, which allows for the volatility of the asset price to change over time in a random manner, as opposed to assuming it is constant, which is a limitation of the classic Black-Scholes model.
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The Heston model couples a geometric asset price to a square-root variance diffusion. Its affine structure gives explicit transforms of the logarithmic asset price, which can be inverted to price European options.