Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment

TL;DR

This paper develops an asymptotic analysis framework to price contingent claim liabilities considering transaction costs, providing explicit expansions and nearly optimal strategies for an exponential utility investor.

Contribution

It rigorously derives asymptotic expansions for the value function and claim prices under transaction costs using utility indifference, extending previous heuristic approaches.

Findings

Asymptotic expansion of the value function around zero transaction costs.

Explicit asymptotic formula for the price of the contingent claim.

Construction of nearly optimal investment strategies.

Abstract

We price a contingent claim liability using the utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of positive proportional transaction cost in two cases with and without a contingent claim liability. Using the computations from the heuristic argument in Whalley & Wilmott we provide a rigorous derivation of the asymptotic expansion of the value function in powers of the transaction cost parameter around the known value function for the case of zero transaction cost in both cases with and without a contingent claim liability. Additionally, using utility indifference method we derive an asymptotic expansion of the price of the contingent claim liability. In both cases, we also obtain a "nearly optimal" strategy, whose expected utility asymptotically matches the leading terms of the value function.