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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year


Cite Score 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.167

Mathematical Citation Quotient (MCQ) 2016: 0.32

Online
ISSN
2196-7040
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Volume 30, Issue 1

Issues

Perpetual American options in a diffusion model with piecewise-linear coefficients

Pavel V. Gapeev / Neofytos Rodosthenous
Published Online: 2013-03-06 | DOI: https://doi.org/10.1524/strm.2013.1135

Abstract

We derive closed form solutions to the discounted optimal stopping problems related to the pricing of the perpetual American standard put and call options in an extension of the Black–Merton–Scholes model with piecewise-constant dividend and volatility rates. The method of proof is based on the reduction of the initial optimal stopping problems to the associated free-boundary problems and the subsequent martingale verification using a local time-space formula. We present explicit algorithms to determine the constant hitting thresholds for the underlying asset price process, which provide the optimal exercise boundaries for the options.

Keywords: Discounted optimal stopping problem; Perpetual American options; Diffusion process with piecewise-linear coefficients; First hitting time; Free-boundary problem

About the article

* Correspondence address: London School of Economics, Department of Mathematics, Houghton Street, London WC2A 2AE, Großbritannien,


Published Online: 2013-03-06

Published in Print: 2013-03-01


Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 30, Issue 1, Pages 1–21, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2013.1135.

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