Option-based portfolio and consumption insurance (OBPCI)

Abstract

This paper examines portfolio insurance (PI) problems for investors who require a minimum level of consumption. Its key contribution is introducing the Option-Based Portfolio and Consumption Insurance (OBPCI) strategy, which extends the popular OBPI framework. As the optimal solution to a constrained utility maximization problem under a general local covariance model, OBPCI is derived using the martingale approach and can be interpreted as a portfolio of options. Given the lack of valid benchmarks involving consumption in the literature, we also introduce and formalize two competitive strategies, optimal on their own, albeit suboptimal to our main problem: the Synthetic Constant Proportion Portfolio and Consumption Insurance (SCPPCI) and the Synthetic Option-Based Portfolio and Consumption Insurance (SOBPCI). Our numerical analysis shows that, under realistic parameters, SCPPCI and SOBPCI can lead to equivalent welfare losses of up to (Formula presented.) for a short investment horizon and (Formula presented.) for low risk aversion, respectively, relative to OBPCI.