The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications

Abstract

AbstractThis article defines and studies a stochastic process that combines two important stylized facts of financial data: reversion to the mean, and a flexible generalized stochastic volatility process: the 4/2 process. This work is motivated by the modeling of at least two financial asset classes: commodities and volatility indexes. We provide analytical expressions for the conditional characteristic functions and closed‐form approximations to relevant cases, in particular a mean‐reverting Heston stochastic volatility model. Our results describe feasible changes of measure with the final aim of pricing financial derivatives. The empirical analysis and the estimation methodology confirm the need of such a model in several examples from the targeted asset classes. Applications to option pricing corroborate the substantial impact on the implied volatility surfaces of the new parameters.