Renewal Equations for Option Pricing

11 Pages Posted: 20 Nov 2007 Last revised: 9 Jul 2008

See all articles by Miquel Montero

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Date Written: November 16, 2007

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.

Suggested Citation

Montero, Miquel, Renewal Equations for Option Pricing (November 16, 2007). Available at SSRN: https://ssrn.com/abstract=1031197 or http://dx.doi.org/10.2139/ssrn.1031197

Miquel Montero (Contact Author)

University of Barcelona - Departament de Física de la Matèria Condensada ( email )

Martí i Franquès, 1
Barcelona, Catalonia 08028
Spain
+34 93 403 92 53 (Phone)
+34 93 402 11 55 (Fax)

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