Option pricing and hedging with minimum local expected shortfall

TL;DR

This paper introduces a Monte-Carlo approach for option pricing and hedging in incomplete markets using expected shortfall, effectively managing tail risks and transaction costs across various stochastic models.

Contribution

It presents a new Monte-Carlo method for option hedging with arbitrary risk criteria, applicable to diverse stochastic processes and incorporating transaction costs.

Findings

Reduces extreme tail risks in fat-tailed distributions

Leads to low Gamma hedging strategies

Transaction costs decrease Gamma of optimal strategies

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.