Option Pricing and Replication with Transactions Costs

TLDR

Transactions costs invalidate the Black‑Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading, and discrete revision using Black‑Scholes deltas generates errors correlated with the market that do not approach zero with more frequent revision when transaction costs are included. The paper develops a modified option‑replicating strategy that accounts for transaction costs and revision frequency. The strategy adjusts replication based on the size of transaction costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision, and the technique permits calculation of transaction costs of option replication and provides bounds on option prices.

Abstract

ABSTRACT Transactions costs invalidate the Black‐Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black‐Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.