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The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications
Author(s) -
EscobarAnel Marcos,
Gong Zhenxian
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2534
Subject(s) - mean reversion , stylized fact , stochastic volatility , econometrics , volatility (finance) , heston model , economics , implied volatility , sabr volatility model , volatility smile , forward volatility , macroeconomics
This 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.