Dynamic Volatility Strategy with Recursive Utility
38 Pages Posted: 13 Mar 2006
Date Written: March 2006
This paper serves two purposes. First, we provide an analytical approximate solution method to solve the optimal consumption and portfolio choice problem for an investor with recursive utility in a complete market. The investment opportunity set is stochastic over time. The problem is solved exactly for special case with unit elasticity of intertemporal substitution, and approximate solution is derived in closed form for more general cases. The solution method provides the same solutions for cases when there exist known analytical solutions. Second, as an important application as well as an illustration of the performance of the solution method, we solve in detail a practical example of Heston's (1993) stochastic volatility model. The market is complete with trading of derivatives, either through options, or pure volatility derivatives such as variance swap. We pay special attention to the new insights that the solution method provides. Specifically we discuss in detail the hedging demand for derivative securities due to the stochastic nature of price volatility. Previous solutions either exclude volatility trading, or assume the expected additive utility without intertemporal consumptions. We calibrate the model to S\&P 500 index and VIX index. The impact of elasticity of intertemporal substitution is separated from that of the risk aversion. We show, contrary to the existing literature on hedging demand of volatility, the effect of the elasticity of intertemporal substitution on hedging demand for derivatives is of first order importance. The investment horizon effect on portfolio choice is also examined.
Keywords: Portfolio Choice, Recursive Utility, Martingale Approach, Stochastic Volatility
JEL Classification: G11, C61, D81
Suggested Citation: Suggested Citation