Portfolio Optimisation with Options: From the Static Replication of CPPI Strategies to a More General Framework

Bernd Scherer

12.1 INTRODUCTION

We finished the last chapter with constant proportion portfolio insurance. This is a well-known example of a continuous trading strategy and its properties have been studied extensively in the literature.¹¹See, for example, Bookstaber and Langsam (2000) or Black and Perold (1992). While the continuous-time framework is predominant in modern finance it is at best an approximation to reality. Even if continuous trading was feasible, the presence of transaction costs would make continuous trading infinitely costly as the sum of absolute stock price increments becomes infinite. Transaction costs will therefore enforce discretisation, ie, the investor rebalances only a finite number of times in an attempt to trade off transaction costs against replication error. Various trading policies to improve this trade-off have been introduced. Instead we want to find a static buy-and-hold strategy of a few traded options that approximates the continuous (and realistically unattainable) constant-proportion portfolio insurance (CPPI) trading strategy as closely as possible. The static option hedge would incur no trading cost and requires no rebalancing. It also takes away the