Option Pricing and Hedging with Small Transaction Costs

Abstract

An investor with constant absolute risk aversion trades a risky asset with general Itôdynamics, 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 indierence prices and hedging strategies in the presence of small transaction costs.

Keywords: transaction costs, indifference pricing and hedging, exponential utility, asymptotics

JEL Classification: G13, G11