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Renewal equations for option pricing

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  • M. Montero

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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  • M. Montero, 2008. "Renewal equations for option pricing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(2), pages 295-306, September.
    • Handle: RePEc:spr:eurphb:v:65:y:2008:i:2:p:295-306
    DOI: 10.1140/epjb/e2008-00349-8
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    1. M. Montero, 2008. "Renewal equations for option pricing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(2), pages 295-306, September.
    2. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955.
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    Cited by:

    1. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Papers 0812.0761, arXiv.org.
    2. Enrico Scalas & Mauro Politi, 2012. "A parsimonious model for intraday European option pricing," Papers 1202.4332, arXiv.org.
    3. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
    4. M. Montero, 2008. "Renewal equations for option pricing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(2), pages 295-306, September.
    5. Xinfeng Ruan & Wenli Zhu & Shuang Li & Jiexiang Huang, 2013. "Equilibrium Asset and Option Pricing under Jump‐Diffusion Model with Stochastic Volatility," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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