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Renewal equations for option pricing

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Miquel 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://arxiv.org/abs/0711.2624
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File URL: http://arxiv.org/pdf/0711.2624
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Publisher Info
Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0711.2624.

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Date of creation: Nov 2007
Date of revision: Jun 2008
Publication status: Published in Eur. Phys. J. B 65, 295-306 (2008)
Handle: RePEc:arx:papers:0711.2624

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