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Renewal equations for option pricing

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Author Info

  • M. Montero

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Abstract

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

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File URL: http://hdl.handle.net/10.1140/epjb/e2008-00349-8
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Bibliographic Info

Article provided by Springer in its journal The European Physical Journal B.

Volume (Year): 65 (2008)
Issue (Month): 2 (September)
Pages: 295-306

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Handle: RePEc:spr:eurphb:v:65:y:2008:i:2:p:295-306

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Web page: http://www.springer.com/economics/journal/10051

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Related research

Keywords: 89.65.Gh Economics; econophysics; financial markets; business and management; 05.40.Fb Random walks and Levy flights; 02.50.Ey Stochastic processes;

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  1. M. Montero, 2008. "Renewal equations for option pricing," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 65(2), pages 295-306, September.
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Cited by:
  1. Scalas, Enrico & Politi, Mauro, 2012. "A parsimonious model for intraday European option pricing," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy.
  2. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Papers 0812.0761, arXiv.org.
  3. Miquel Montero, 2007. "Renewal equations for option pricing," Papers 0711.2624, arXiv.org, revised Jun 2008.

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