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Discrete-Time Hedging for European Contingent Claims via Risk Minimization in Market Measure

Drishtikon: A Management Journal

Volume 2 Issue 1

Published: 2010
Author(s) Name: Easwar Subramanian, Vijaysekhar Chellaboina, Anil Bhatia, Sanjay P. Bhat
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Abstract

In this work, we propose a discrete-time hedging strategy for a European contingent claim (ECC) that reduces risk in the market measure. To this end, we minimize the second-moment of the hedging error in the market measure and give computable expressions for the positions that the seller must hold in the underlying asset (of the ECC) at any given hedge time. The minimization of the second-moment of the hedging error also yields an expression for the price of the option. The expressions obtained can be evaluated using Monte-Carlo methods. A noteworthy feature of the framework is that, it does not assume any specific model for the underlying asset price or involve any assumptions on the underlying market probability measure. Keywords: European Contingent Claims (ECC), Discrete-time hedging, Market measure, Second-moment, Risk-minimization, Path-dependent options, Martingale measure, Geometric Brownian motion (GBM)

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