An Application of Damped Diffusion for Modeling Volatility Dynamics
提出阻尼常数弹性方差随机波动率模型，解决CEV模型爆炸问题并更好刻画均值回复，基于VIX推断潜在方差，用S&P500数据实证显示样本内拟合和样本外方差预测及期权定价均优于CEV和Heston模型。
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.