Memory in the Black-Scholes model

• Author(s): Ferreira, J. A. ; Oliveira, P. de
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11201
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Black-Scholes equation; Fick’s flux; Non-Fickian flux; Integro-differential equation
• Document Type: Preprint
• Language: English

Description

The evolution in time of European options is usually studied using the Black-Scholes formula. This formula is obtained from the equivalence between the Black-Scholes equation and a heat equation. The solution of the last equation presents infinite speed of propagation which induces the same property for European options. In this paper we study integro-differential equations which can be used to describe the evolution of European options and which is established replacing the heat equation by a delayed heat equation. Center for Mathematics of University of Coimbra; Project PTDC/MAT/74548/2006