Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods

Abstract

The constant elasticity of variance (CEV) model is widely studied and applied for volatility forecasting and optimal decision making in both areas of financial engineering and operational management, especially in option pricing, due to its good fitting effect for the volatility process of various assets such as stocks and commodities. However, it is extremely difficult to conduct parameter estimation for the CEV model in practice since the precise likelihood function cannot be derived. Motivated by the gap between theory and practice, this paper initiatively applies the Markov Chain-Monte Carlo (MCMC) method into parameter estimation for the CEV model. We first construct a theoretical structure on how to implement the MCMC method into the CEV model, and then execute an empirical analysis with big data of CSI 300 index collected from the Chinese stock market. The final empirical results reveal insights on two aspects: On one aspect, the simulated results of the convergence test are convergent, which demonstrates that the MCMC estimation method for the CEV model is effective; On the other aspect, by a comparison with other two most frequently used estimation methods, the maximum likelihood estimation (MLE) and the generalized moment estimation (GMM), our method is proved to be of high accuracy and has a simpler implementation and wider application.