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June 2015 American option valuation under continuous-time Markov chains
B. Eriksson, M. R. Pistorius
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Adv. in Appl. Probab. 47(2): 378-401 (June 2015). DOI: 10.1239/aap/1435236980

Abstract

This paper is concerned with the solution of the optimal stopping problem associated to the value of American options driven by continuous-time Markov chains. The value-function of an American option in this setting is characterised as the unique solution (in a distributional sense) of a system of variational inequalities. Furthermore, with continuous and smooth fit principles not applicable in this discrete state-space setting, a novel explicit characterisation is provided of the optimal stopping boundary in terms of the generator of the underlying Markov chain. Subsequently, an algorithm is presented for the valuation of American options under Markov chain models. By application to a suitably chosen sequence of Markov chains, the algorithm provides an approximate valuation of an American option under a class of Markov models that includes diffusion models, exponential Lévy models, and stochastic differential equations driven by Lévy processes. Numerical experiments for a range of different models suggest that the approximation algorithm is flexible and accurate. A proof of convergence is also provided.

Citation

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B. Eriksson. M. R. Pistorius. "American option valuation under continuous-time Markov chains." Adv. in Appl. Probab. 47 (2) 378 - 401, June 2015. https://doi.org/10.1239/aap/1435236980

Information

Published: June 2015
First available in Project Euclid: 25 June 2015

zbMATH: 06458824
MathSciNet: MR3360382
Digital Object Identifier: 10.1239/aap/1435236980

Subjects:
Primary: 91G20
Secondary: 60J27 , 65C40

Keywords: American option , Feller process , free-boundary problem , Markov chain , numerical approximation , Optimal stopping

Rights: Copyright © 2015 Applied Probability Trust

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Vol.47 • No. 2 • June 2015
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