Asymptotically optimal discretization of hedging strategies with jumps

TL;DR

This paper develops an asymptotic framework for optimizing the timing of discrete hedging trades in models with jumps, aiming to minimize hedging error relative to trading costs.

Contribution

It extends existing methods to jump models and derives explicit optimal discretization rules based on hitting times.

Findings

Explicit formulas for optimal hitting time discretization rules

Asymptotic minimization of hedging error in jump models

Framework applicable to large cost regimes

Abstract

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean square discretization error for a smaller cost. We focus on discretization rules based on hitting times and give explicit expressions for the optimal rules within this class.