Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model and Applications to American Options

TL;DR

This paper develops a new class of reflected backward stochastic differential equations driven by martingales in a finite state Markov chain setting, and applies them to model American options with stochastic discounting.

Contribution

It introduces a novel type of RBSDEs driven by martingales in Markov chains and demonstrates their application to American option pricing with stochastic discount functions.

Findings

Existence and uniqueness of solutions for the new RBSDEs.

Existence of a unique constrained super-hedging strategy for American options.

Application of RBSDE theory to American options in Markov chain models.

Abstract

In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the new equations. Then we discuss American options in a finite state Markov chain model, in the presence of a stochastic discount function (SDF) and using the theory of the new RBSDEs. We show that there exists a constrained super-hedging strategy for an American option, which is unique in our framework as the solution to an RBSDE.