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Stochastic Approximation Methods for American Type Options
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 6, 1607-1631 p.Article in journal (Refereed) Published
Abstract [en]

Stochastic approximation methods for rewards of American type options are studied. Pay-off functions are non random possibly discontinuous functions or random càdlàg functions. General conditions of convergence for binomial, trinomial, and skeleton reward approximations are formulated. Underlying log-price processes are assumed to be random walks. These processes are approximated by log-price processes given by random walks with discrete distributions of jumps. Backward recurrence algorithms for computing of reward functions for approximating log-price processes are given. These approximation algorithms and their rates of convergence are numerically tested for log-price processes represented byGaussian and compoundGaussian random walks. Comparison of the above approximation methods is made.

Place, publisher, year, edition, pages
2016. Vol. 45, no 6, 1607-1631 p.
Keyword [en]
American type option, Binomial approximation, Compound Gaussian random walk, Convergence of rewards, Gaussian random walk, Geometric random walk, Markov log-price process, Random pay-off, Rate of convergence, Reward function, Skeleton approximation, Trinomial approximation, Primary: 91G20, 91G60, 60J22, Secondary: 65C40, 62L15
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-127846DOI: 10.1080/03610926.2014.915046ISI: 000372556000003OAI: oai:DiVA.org:su-127846DiVA: diva2:911572
Conference
15th Conference on Applied Stochastic Models and Data Analysis (ASMDA), Barcelona, Spain, 2013
Available from: 2016-03-13 Created: 2016-03-13 Last updated: 2016-04-25Bibliographically approved

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Silvestrov, Dmitrii
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Department of Mathematics
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