3. Proportional Transaction Costs: An Introduction

This chapter reviews the limited literature on option pricing in the presence of transaction costs outside the stochastic dominance (SD) approach. It starts by pointing out the importance of the topic, given the indeterminacy in defining the “true” price of a traded option because of the wide bid-ask spreads observed in the option markets. It then summarizes the studies that demonstrate the failure of the no arbitrage approach even when the underlying market is complete and there are transaction costs in trading the underlying asset. Last, it presents the generic investor’s dynamic asset allocation problem between a risky and a riskless asset given proportional transaction costs on the risky asset and derives the no transaction zone when the dynamics of the risky asset tend to diffusion or jump diffusion. These are inputs for the application of the SD approach to option pricing under transaction costs.