Renewal equations for option pricing
Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
Corresponding author: a firstname.lastname@example.org
Revised: 30 June 2008
Published online: 17 September 2008
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.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 05.40.Fb – Random walks and Levy flights / 02.50.Ey – Stochastic processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008