Risk-return arguments applied to options with trading costs

TL;DR

This paper develops a framework for option pricing and hedging based on risk-return utility functions, incorporating transaction costs perturbatively to determine rational prices and strategies.

Contribution

It introduces a novel approach to option valuation that explicitly accounts for risk, return, and transaction costs within a utility maximization framework.

Findings

Optimal strategies are derived explicitly without transaction costs.

Transaction costs are incorporated as a first-order perturbation.

Rational option prices are determined considering both buyer and writer perspectives.

Abstract

We study the problem of option pricing and hedging strategies within the frame-work of risk-return arguments. An economic agent is described by a utility function that depends on profit (an expected value) and risk (a variance). In the ideal case without transaction costs the optimal strategy for any given agent is found as the explicit solution of a constrained optimization problem. Transaction costs are taken into account on a perturbative way. A rational option price, in a world with only these agents, is then determined by considering the points of view of the buyer and the writer of the option. Price and strategy are determined to first order in the transaction costs.