Martingale Representations and Hedge Ratios

  • Eckhard PlatenEmail author
  • Nicola Bruti-Liberati
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 64)


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.


Option Price Contingent Claim Valuation Function Geometric Brownian Motion Asian Option 
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  1. Heath, D. (1995). Valuation of derivative securities using stochastic analytic and numerical methods, PhD thesis, ANU, Canberra. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Finance and Economics, Department of Mathematical SciencesUniversity of Technology, SydneyBroadwayAustralia

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