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CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES
Author(s) -
Mijatović Aleksandar,
Pistorius Martijn
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00486.x
Subject(s) - markov chain , markov process , barrier option , markov model , markov renewal process , computer science , range (aeronautics) , convergence (economics) , jump , variable order markov model , mathematical optimization , mathematics , econometrics , economics , statistics , engineering , physics , machine learning , quantum mechanics , economic growth , aerospace engineering
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.