商品市场的可变波动率弹性模型

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