Portfolio optimization and dynamic hedging with receding horizon control, stochastic programming, and Monte Carlo simulation.

摘要

We develop a new methodology to attack the two classic finance problems of portfolio optimization and dynamic hedging in an environment with a multi-period horizon, transaction costs, and dynamic asset parameters. Both of these problems would ideally be solved with dynamic programming, a methodology that would deliver the optimal solution. However, even problems that are much smaller than those of realistic size are computationally infeasible when formulated as a dynamic program. Thus, we propose a methodology to approximate the optimal solution to these computationally infeasible dynamic programming problems. Our methodology is based upon the optimization techniques of receding horizon control and stochastic programming. Bringing these methodologies together allows us to combine the long horizon of dynamic programming with computational feasibility. This methodology breaks down the monolithic dynamic programming problem into a sequence of smaller problems solved over time which allows us to incorporate changes in the system dynamics and to overcome issues of computational complexity.; Our methodology has several key advantages. It can be applied to (1) a wide variety of asset dynamics, (2) more than just one or two assets (some competing methodologies are limited to one or two assets), (3) different performance objectives, (4) environments that include realistic factors such as transaction costs. Its final advantage is (5) its strong performance vs. competitors as we are able to show significantly superior results with our methodology.; When applied to the dynamic hedging problem of hedging a short position on a derivative, this methodology is applicable to vanilla options, where analytical approximations exist, and to multi-dimensional options where no analytical solutions exist. Through simulation, empirical analysis, and a theoretical justification, we show our methodology significantly reduces expected absolute hedging error and increases expected utility on vanilla options vs. the classic analytical solutions as well as on multi-dimensional options vs. heuristic methodologies. For portfolio optimization, we focus mainly on optimizing a portfolio of defaultable bonds following a doubly stochastic reduced form model. Through Monte Carlo simulation we demonstrate results showing our methodology can significantly outperform the bond portfolio methodology of holding a constant percentage of the portfolio in each bond.