Berlin 2008 – wissenschaftliches Programm

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 13: Poster Session (posters on display 10:00-19:00)

AKSOE 13.9: Poster

Mittwoch, 27. Februar 2008, 17:30–19:00, Poster G

Renewal equations for option pricing — •Miquel Montero — Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain.

We will present an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW). This setup enhances the potential use of CTRW techniques and results in finance.

We solve the equations for several contract specifications (European binary calls, European vanilla calls, American binary puts, perpetual American vanilla puts), by obtaining explicit expressions for a particular but exemplifying jump probability density function: an asymmetric exponential.

We present plots that depict the properties of the option prices for different values of the free parameters, and show how one can recover the celebrated results for the Wiener process under certain limits.