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On the Pricing of American Options in Exponential Lévy Markets

Part of: Mathematical economics Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Roman V. Ivanov
Roman V. Ivanov*
Affiliation:
Institute of Control Sciences of Russian Academy of Sciences
*
∗ Postal address: Laboratory 38, Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya 65, 117997 Moscow, Russia. Email address: roivanov@yahoo.com
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Abstract

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In this paper, we discuss the problem of the pricing of American-style options in the exponential Lévy security market model. This model is typically incomplete, and we derive the explicit bounds of the interval of no arbitrage prices and the related optimal stopping moments for American put options and American call options in both finite and infinite horizon time. We consider a large class of Lévy processes.

Keywords

Incomplete market; Lévy processAmerican optionupper pricelower priceoptimal stopping

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J75: Jump processes 91B70: Stochastic models
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 409 - 419
Copyright
Copyright © Applied Probability Trust 2007 

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