Narrow Results

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.

In this paper we investigate whether a CEV model can account for the observed variation in the at-the-money implied volatility as a function of the level of the at-the-money forward rate. We also determine which exponent β in the CEV process for the swap rate best accounts for the observed behaviour of the implied volatilities.

An arbitrage-free CEV economy driven by Brownian motion in independent, continuous random time is introduced. European options are priced by the no-arbitrage principle as conditional averages of their classical CEV values over the CEV-modified random time to maturity. A novel representation of the classical CEV price is used to investigate the asymptotics of the average implied volatility. It is shown that the average implied volatility of the at-the-money call option is lower and of deep out-of-the-money call options, under appropriate sufficient conditions, greater than the implied CEV volatilities. Unlike in the classical CEV model, the shape of the out-of-the-money tail can be both downward and upward sloping depending on the tails of random time. The model is implemented in limit lognormal time. Its multiscaling law is shown to imply a term structure of implied volatility that is qualitatively more sensitive to changes in the time to maturity than is the classical CEV model.

In this paper, we extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse $\alpha$-stable subordinator. The new model can capture the subdiffusive characteristics of financial markets. We find the corresponding fractional Fokker–Planck equation governing the PDF of the new process. We also derive the analytical formula for option prices in terms of eigenfunction expansion. This method avoids the evaluation of PDF of an inverse $\alpha$-stable variable and also eliminates the need for numerical integration to calculate the option prices. We numerically investigate the sensitivities of the option prices to the key parameters of the newly developed model.