Beschreibung:
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 tosignificantly reduce extreme risks, and generically leads to low Gamma hedging.Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy