Dynamic Volatility Strategy with Recursive Utility

In this article, an analytical approximate solution method is given to provide investors with the means to make optimal consumption and portfolio choices with recursive utility in a complete market. The investment opportunity set is stochastic over time. The method is used to provide an exact determination of the unit elasticity of intertemporal substitution. An approximate solution method is derived in closed form for more general applications. The solution method is shown to provide the same solutions for cases with known analytical solutions, thus proving its effectiveness. Heston’s (1993) stochastic volatility model is solved in detail as a practical and important illustration of the solution method. The market is complete with trading of derivatives, through either options or pure volatility derivatives such as variance swap. New insights gained from the solution method, such as the hedging demand for derivative securities due to the stochastic nature of price volatility, are detailed and discussed. Previous solutions have either excluded volatility trading or assumed the expected additive utility without intertemporal consumption. The model is calibrated to the S&P 500 index and VIX index. The impact of elasticity of intertemporal substitution is separated from that of risk aversion. Contrary to existing literature on the hedging demand of volatility, the effect of the elasticity of intertemporal substitution on hedging demand for derivatives is proven to be of first-order importance. The investment horizon effect on portfolio choice is also examined.