Option Pricing and Hedging with Small Transaction Costs

TL;DR

This paper develops asymptotic formulas for optimal trading, utility indifference prices, and hedging strategies for an investor with constant absolute risk aversion trading a risky asset with small transaction costs.

Contribution

It derives a leading-order optimal trading policy and welfare in a general Itô-dynamics setting, extending to cases with random endowment.

Findings

Explicit asymptotic formulas for utility indifference prices.

Optimal trading policy accounting for small transaction costs.

Quantitative insights into hedging strategies under transaction costs.

Abstract

An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.