Arbitrage-Free Pricing of Game Options in Nonlinear Markets

TL;DR

This paper extends the nonlinear arbitrage-free pricing framework for game options, providing detailed analysis of pricing, hedging, and exercising strategies, and introduces a BSDE approach for explicit solutions.

Contribution

It advances the understanding of game options in nonlinear markets by integrating a BSDE methodology and analyzing American-style contracts.

Findings

Detailed study of unilateral pricing and hedging strategies

Explicit solutions via doubly reflected BSDEs under certain conditions

Extension of previous models to more general nonlinear setups

Abstract

The goal is to re-examine and extend the findings from the recent paper by Dumitrescu, Quenez and Sulem (2017) who studied game options within the nonlinear arbitrage-free pricing approach developed in El Karoui and Quenez (1997). We consider the setup introduced in Kim, Nie and Rutkowski (2018) where contracts of an American style were examined. We give a detailed study of unilateral pricing, hedging and exercising problems for the counterparties within a general nonlinear setup. We also present a BSDE approach, which is used to obtain more explicit results under suitable assumptions about solutions to doubly reflected BSDEs.