2003/08/27 by Benoît Pochart, Pochart, Benoît, Jean‐Philippe Bouchaud +2
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed Matter (cond-mat) #FOS: Physical sciences #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/0308570
23 pages, 7 figures, 8 tables
arxiv created 2003/08/27 · openalex publication_date 2003/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.