A generalized constant elasticity of volatility and correlation ratio (CEVC) model: Empirical evidence and application for portfolio optimization

Abstract

This study developed a multivariate continuous-time model enabling a generalized constant elasticity of volatility (CEV) model on the marginal and a new stylized fact named constant elasticity of correlation ratio (CEC) in the dependence structure. Therefore, the entire structure is called the generalized constant elasticity of volatility and correlation ratio (CEVC) model. The model inherited the usefulness of the one-dimensional CEV model for pricing and portfolio optimization purposes. It enhances this model to ensure better-behaved volatility of returns. A unique weak solution exists for the multidimensional stochastic differential equations. Empirical analysis indicates the significance of the elasticity parameters driving the CEVC model and insights into the dynamics of volatilities and correlations. We estimated the embedded n-dimensional generalized CEV model (i.e., no CEC), the CEC model (i.e., no CEV), and the geometric Brownian motion (GBM, no CEC or CEV). The model was applied to portfolio optimization based on expected utility theory. The findings yield closed-form solutions for optimal strategies and value functions compared to other models.