Linear vector optimization and European option pricing under proportional transaction costs

TL;DR

This paper compares two linear vector optimization methods for pricing European options with proportional transaction costs, establishing their equivalence through geometric duality and support function analysis.

Contribution

It demonstrates the equivalence of two different optimization approaches for option pricing under transaction costs using geometric duality theory.

Findings

Established the equivalence of the two optimization methods.

Linked support functions of primal and dual problems.

Provided insights into superhedging under transaction costs.

Abstract

A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Lohne & Rudloff (2014) is compared to a special case of the algorithms for American type derivatives due to Roux & Zastawniak (2014). An equivalence between these two approaches is established by means of a general result linking the support function of the upper image of a linear vector optimisation problem with the lower image of the dual linear optimisation problem.