CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES

Aleksandar Mijatović · Martijn R. Pistorius

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Stochastic processes and financial applications Financial Markets and Investment Strategies Probability and Risk 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 Lévy process and a local volatility jump‐diffusion. We also provide a convergence proof and error estimates for this algorithm.

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References

2003Financial Modelling with Jump Processes 2003Limit Theorems for Stochastic Processes 2002A Jump-Diffusion Model for Option Pricing 2002The Fine Structure of Asset Returns: An Empirical Investigation 1990Numerical Methods for Stochastic Control Problems in Continuous Time 1997Processes of normal inverse Gaussian type 1995Hyperbolic Distributions in Finance 2004Option Pricing Under a Double Exponential Jump Diffusion Model

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