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A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility

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  • Dorival Le~ao
  • Alberto Ohashi
  • Vinicius Siqueira

Abstract

In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and constructive methodology which allows us to compute pure hedging strategies w.r.t arbitrary square-integrable claims in incomplete markets. In particular, the methodology can be applied to quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. We illustrate the method with numerical examples based on generalized Follmer-Schweizer decompositions, locally-risk minimizing and mean-variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.

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  • Dorival Le~ao & Alberto Ohashi & Vinicius Siqueira, 2013. "A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility," Papers 1308.1704, arXiv.org, revised Aug 2013.
    • Handle: RePEc:arx:papers:1308.1704
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    References listed on IDEAS

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