An Application of Damped Diffusion for Modeling Volatility Dynamics.

This article introduces the damped constant elasticity variance (DCEV) stochastic volatility model, designed to improve upon the traditional constant elasticity variance (CEV) and nonlinear drift (NLD) stochastic volatility models by preventing explosive variance behavior and better capturing mean-reverting dynamics. The DCEV model retains a linear drift term, enabling an analytic formula to infer latent variances from VIX levels and allowing simultaneous maximum-likelihood estimation of physical and risk-neutral parameters using S&P 500 returns and inferred variances. Empirical analyses using data from 1996 to 2017 demonstrate that the DCEV model outperforms the CEV and NLD models in in-sample fitting and out-of-sample variance forecasting, and surpasses both the CEV and Heston’s square root (SQR) models in out-of-sample option pricing accuracy. The study highlights the DCEV model’s suitability for describing volatility dynamics and suggests its potential for broader applications in financial modeling.