The Variable Volatility Elasticity Model from Commodity Markets

In this paper, we propose and study a novel continuous-time model, based on the well-known constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model can not be treated as a constant from the perspective of stochastic analysis. To address this issue, we deduce the price process of assets from the perspective of volatility elasticity, propose the constant volatility elasticity (CVE) model, and further derive a more general variable volatility elasticity (VVE) model. Moreover, our model can describe the positive correlation between volatility and asset prices existing in the commodity markets, while CEV model can only describe the negative correlation. Through the empirical research on the financial market, many assets, especially commodities, often show this positive correlation phenomenon in some time periods, which shows that our model has strong practical application value. Finally, we provide the explicit pricing formula of European options based on our model. This formula has an elegant form convenient to calculate, which is similarly to the renowned Black-Scholes formula and of great significance to the research of derivatives market.