Option pricing and hedging with minimum local expected shortfall

Benoît Pochart (1) , Jean-Philippe Bouchaud (2)

1 CMAP - Centre de Mathématiques Appliquées
2 SPEC - UMR3680 - Service de physique de l'état condensé

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.

Domaines: Autre [cond-mat.other]

Benoît Pochart, Jean-Philippe Bouchaud. Option pricing and hedging with minimum local expected shortfall. 2003. ⟨hal-00133198⟩