Martingale Representations and Hedge Ratios

Abstract

The calculation of hedge ratios is fundamental to both the valuation of derivative securities and also the risk management procedures needed to replicate these instruments. In Monte Carlo simulation the following results on martingale representations and hedge ratios will be highly relevant. In this chapter we follow closely Heath (1995) and consider the problem of finding explicit Itô integral representations of the payoff structure of derivative securities. If such a representation can be found, then the corresponding hedge ratio can be identified and numerically calculated. For simplicity, we focus here on the case without jumps. The case with jumps is very similar.