In honour of Max Planck (1858–1947) on the occasion of his 150th birthday.
Option pricing theory for financial assets with memory†
Version of Record online: 4 FEB 2008
Copyright © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 17, Issue 2-3, pages 130–141, February 2008
How to Cite
Schulz, M. (2008), Option pricing theory for financial assets with memory. Ann. Phys., 17: 130–141. doi: 10.1002/andp.200710280
- Issue online: 4 FEB 2008
- Version of Record online: 4 FEB 2008
- Manuscript Received: 5 NOV 2007
- non-Markov processes;
- option pricing theory
Diffusion processes play an important role in physics as well as in financial sciences. The usual description by stochstic differential equations considers the Wiener process as external stochastic term, while the deterministic drift term is local in time. However, the complexity of the interaction between the observed diffusive degree of freedom and the hidden dynamics of the whole system, e.g., the coupling between a certain particle and the surrounding liquid or the relations between the price of a financial asset and the global market, requires the consideration of possible memory effects.
In the present paper we analyze the effects of a non-Markovian asset price model on the corresponding European option prices. This model considers drift terms which are non-local in time, so that memory effects appear. As the main result we present a generalized Black-Scholes equation considering the whole history of the asset price evolution.