Small transaction cost asymptotics and dynamic hedging

Transaction costs are one of the major impediments to the implementation of dynamic hedging strategies. We consider an alternative to utility maximization, similar to the “good-deal” pricing framework in incomplete markets. We perform a dynamic riskreward analysis for a family of non-self-financing strategies of practical importance: deterministic time hedging; i.e., hedging at predetermined, fixed, times. In the limit of small relative transaction costs, we carry out the asymptotic analysis and find that transaction costs affect the hedge ratios and that the time between trades is related in a simple way to the local sensitivities of the replication target. ∗Acknowledgments: We would like to acknowledge the helpful comments and suggestions of seminar participants at the University of Toronto, the Fields Institute, Université de Rennes I, Université de Paris VI, University of Texas at Austin, Swiss Federal Institutes of Technology in Zürich and Lausanne. We would also like to thank Peter Bossaerts, Peter Carr, Patrick Jaillet, Ehud Ronn, and Klaus Toft, for discussions and suggestions. Part of this work was completed when both authors were at the University of Toronto. †Department of Mathematics, Imperial College, London, SW7 2AZ, United Kingdom, [email protected] ‡Corresponding author. IROM Department, McCombs School of Business, University of Texas at Austin, 1 University Station, B6500, Austin, TX 78712-1175, [email protected]