  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.
