Continuously monitored barrier options under Markov processes

TL;DR

This paper introduces an algorithm for pricing barrier options in one-dimensional Markov models by constructing an approximating Markov chain, with convergence proof and applications to various models.

Contribution

It presents a novel algorithm for barrier option pricing using Markov chain approximation, applicable to complex models like Levy processes and jump-diffusions.

Findings

Algorithm accurately prices barrier options in diverse Markov models.

Convergence proof and error estimates validate the method.

Implementation demonstrated on local Levy and jump-diffusion models.

Abstract

In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local Levy process and a local volatility jump-diffusion. We also provide a convergence proof and error estimates for this algorithm.