基于证券和VIX衍生品的投资优化策略

Optimal investment in equity and VIX derivatives

基于带跳跃的随机波动率模型,得到了包含股票资产和VIX衍生品的投资组合优化策略的解析解。我们的模型考虑了存在扩散风险、波动性风险以及跳跃风险这三类风险时,完全市场与不完全市场情况下投资策略的业绩表现。与股票衍生品相比,VIX衍生品允许直接暴露于波动性风险。基于解析解的公式,明确地确定了纳入VIX衍生品所带来的投资组合改善,并在理论上确定其为正数。这证明了在投资组合管理环境中对VIX衍生品的经济直觉和观察到的需求。数值例子说明了这些结果。

We solve in closed-form the optimal investment strategies in equity and VIX derivatives in a stochastic volatility model with jumps.Our framework includes both complete market and incomplete market cases,when diffusive risk,volatility risk and jump risk are present.VIX derivatives allow for direct exposure to volatility risk compared to equity derivatives.Based on the closed-form formulas,we explicitly determine the portfolio improvements brought by the inclusion of the VIX derivatives and establish that it is theoretically positive.This justifies the economic intuition and observed demand for VIX derivatives in a portfolio management setting.Numerical examples illustrate the results.