Convergence of option rewards for Markov type price processes modulated by stochastic indices. II

Authors:
D. S. Silvestrov, H. Jönsson and F. Stenberg

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **80** (2009).

Journal:
Theor. Probability and Math. Statist. **80** (2010), 153-172

MSC (2000):
Primary 60J05, 60H10; Secondary 91B28, 91B70

Published electronically:
August 20, 2010

MathSciNet review:
2541960

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as a stochastic index modulating the price component. American type options with pay-off functions, which admit upper bounds of a power type, are studied. Both the transition characteristics of the price processes and the pay-off functions are assumed to depend on a perturbation parameter and to converge to the corresponding limit characteristics as . In the first part of the paper, asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models are given. In the second part of the paper, these skeleton approximations are used for getting results about the convergence of reward functionals for American type options for perturbed price processes with discrete and continuous time. Examples related to modulated exponential price processes with independent increments are given.

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Additional Information

**D. S. Silvestrov**

Affiliation:
Mälardalen University, Västerås, Sweden

Email:
dmitrii.silvestrov@mdh.se

**H. Jönsson**

Affiliation:
Eurandom, Eindhoven University of Technology, The Netherlands

Email:
jonsson.@eurandom.tue.nl

**F. Stenberg**

Affiliation:
Nordea Bank, Stockholm, Sweden

Email:
fredsten@kth.se

DOI:
http://dx.doi.org/10.1090/S0094-9000-2010-00802-7

Keywords:
Reward,
convergence,
optimal stopping,
American option,
skeleton approximation,
Markov process,
price process,
modulation,
stochastic index

Received by editor(s):
August 25, 2008

Published electronically:
August 20, 2010

Article copyright:
© Copyright 2010
American Mathematical Society