Convergence of option rewards for Markov type price processes modulated by stochastic indices. II
Authors:
D. S. Silvestrov, H. Jönsson and F. Stenberg
Journal:
Theor. Probability and Math. Statist. 80 (2010), 153-172
MSC (2000):
Primary 60J05, 60H10; Secondary 91B28, 91B70
DOI:
https://doi.org/10.1090/S0094-9000-2010-00802-7
Published electronically:
August 20, 2010
MathSciNet review:
2541960
Full-text PDF Free Access
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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 $\delta \geq 0$ and to converge to the corresponding limit characteristics as $\delta \to 0$. 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.
References
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References
- D. S. Silvestrov, H. Jönsson, and F. Stenberg, Convergence of option rewards for Markov type price processes modulated by stochastic indices. I, Teor. Ĭmovir. ta Matem. Statyst. 79 (2009), 138–154. MR 2494545 (2010e:60151)
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- H. Jönsson, A. G. Kukush, and D. S. Silvestrov, Threshold structure of optimal stopping strategies for American type options. I, Theor. Ĭmovir. ta Matem. Statyst. 71 (2004), 113–123; English transl. in Theory Probab. Math. Statist. 71 (2005), 93–103. MR 2144323 (2006h:91075)
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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
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