Conservative delta hedging under transaction costs

TL;DR

This paper develops explicit robust hedging strategies for convex and concave payoffs under small transaction costs, combining conservative delta hedging and enlarging volatility, with asymptotic analysis of errors.

Contribution

It introduces a novel approach combining Mykland's conservative delta hedging with Leland's enlarging volatility, using specific rebalancing times for improved super-hedging under uncertainty.

Findings

Super-hedging bounds are established for convex and concave payoffs.

A central limit theorem for super-hedging error as transaction costs vanish.

Analysis of mean squared error of the hedging strategies.

Abstract

Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative volatility enable us to super-hedge convex and concave payoffs respectively. The idea is a combination of Mykland's conservative delta hedging and Leland's enlarging volatility. We use a specific sequence of stopping times as rebalancing dates, which can be superior to equidistant one even when there is no model uncertainty. A central limit theorem for the super-hedging error as the coefficient of linear transaction costs tends to zero is proved. The mean squared error is also studied.