An Application of Damped Diffusion for Modeling Volatility Dynamics

Abstract

This paper proposes a damped constant elasticity variance (CEV) stochastic volatility (DCEV) model, which remedies the possible explosive behavior of the CEV model and also accommodates the mean-reverting dynamics more appropriately than the nonlinear drift (NLD) stochastic volatility model. As the DCEV model maintains the linear drift, an analytic formula is available to efficiently infer latent variances from VIX levels, after which both its physical and risk-neutral parameters can be simultaneously estimated with the maximum-likelihood approach given S&P 500 returns and inferred variances. The DCEV model outperforms the CEV and NLD models in in-sample fitting performance and in out-of-sample variance forecasting under the physical measure. It also exhibits superior ability in out-of-sample option pricing over the CEV and Heston’s (1993) models under the risk-neutral measure. This satisfactory performance demonstrates the suitability of describing volatility dynamics with the DCEV model and the potential of applying this to study other issues.