Asymptotic replication with modified volatility under small transaction costs

TL;DR

This paper develops a continuous control hedging strategy for European options under local volatility with small transaction costs, proving a central limit theorem for hedging error and optimizing error variance.

Contribution

It introduces a novel continuous control approach that asymptotically replicates options payoff under small transaction costs, extending Leland's strategy.

Findings

Hedging error follows a central limit theorem.

Explicit trading strategy minimizes asymptotic error variance.

Strategy effectively replicates payoff with small transaction costs.

Abstract

Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An associated central limit theorem of hedging error is proved. The asymptotic error variance is minimized by an explicit trading strategy.