Applications of weak convergence for hedging of game options

TL;DR

This paper proves that the values of Dynkin's games with path-dependent payoffs converge when underlying processes converge weakly, enabling approximation of continuous-time game option prices via discrete models with broader applicability.

Contribution

It establishes convergence of Dynkin's game values under extended weak convergence, allowing for more general payoff functions and process conditions in option pricing.

Findings

Dynkin's game values converge under extended weak convergence.

Discrete time models can approximate continuous-time game options.

Results apply to more general payoffs and process conditions.

Abstract

In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^{\infty}$ to the Dynkin's game value corresponding to $S$. We use these results to approximate game options prices with path dependent payoffs in continuous time models by a sequence of game options prices in discrete time models which can be calculated by dynamical programming algorithms. In comparison to previous papers we work under more general convergence of underlying processes, as well as weaker conditions on the payoffs.