Abstract

In this article we consider the problem of tracking the value of a ‘target’ portfolio of European options with a range of maturities within a one year planning horizon using dynamic replicating strategies involving a small subset of the options. In defining a dynamic replicating strategy we only allow rebalancing decision points for the replicating portfolio at the payout dates of the options in the target, but for one application we measure the tracking error between the value of the two portfolios daily. The target portfolio value has a Bermudan path-dependency at these decision points and it is likely that a carefully chosen dynamic strategy will out-perform simpler static or quasi-static strategies. Here we construct trading strategies by solving appropriate stochastic programming formulations of two principal tracking problems: portfolio compression for risk management calculations and dynamic replicating strategies for simplified replicating portfolios which may be used for hedging or actual target portfolio simplification. We demonstrate the superior performance of dynamic strategies relative to both more static strategies and delta hedging in a number of numerical tests.

Introduction

In this article we construct periodically rebalanced dynamic trading strategies for a portfolio containing a small number of tradable instruments which tracks the value of a large ‘target’ portfolio daily over a long period of time. A successful solution to this ‘tracking’ problem is useful in a number of practical financial applications.