Risk Minimization for Game Options in Markets Imposing Minimal Transaction Costs

TL;DR

This paper investigates optimal hedging strategies for game options in markets with minimal transaction costs, providing theoretical proofs and numerical methods within continuous and binomial models.

Contribution

It introduces a new approach to minimize shortfall risk for game options considering minimal transaction costs, with proofs in the Black--Scholes model and numerical schemes via binomial models.

Findings

Existence of a risk-minimizing trading strategy in the BS model.

Development of numerical schemes for risk calculation.

Insights into the impact of minimal transaction costs on hedging strategies.

Abstract

We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction costs. We prove that in the continuous time Black--Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.