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Option pricing and hedging with minimum local expected shortfall

Benoît Pochart·Jean-Philippe Bouchaud
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Abstract

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the presence of transaction costs. We illustrate the method on plain vanilla options when the price returns follow a Student-t distribution. We show that in the presence of fat-tails, our strategy allows to significantly reduce extreme risks, and generically leads to low Gamma hedging. Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy.

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Benoît Pochart, Jean-Philippe Bouchaud. 2003-08-27. Option pricing and hedging with minimum local expected shortfall. https://arxiv.org/abs/cond-mat/0308570

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