Document 
Eur. Phys. J. B 42, 141-153 (2004)
DOI: 10.1140/epjb/e2004-00366-7
Partial derivative approach for option pricing in a simple stochastic volatility model
M. MonteroDepartament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
miquel.montero@ub.edu
(Received 12 December 2003 / Received in final form 13 May 2004 / Published online 26 November 2004)
Abstract
We study a market model in which the volatility of the stock may jump at a random time
from a fixed value
to another fixed value.
This model has already been introduced in the literature. We present a new approach to the problem, based on partial differential
equations, which gives a different perspective to the issue. Within our framework we can easily consider several forms for
the market price of volatility risk, and interpret their financial meaning. We thus recover solutions previously mentioned
in the literature as well as obtaining new ones.
02.30.Jr - Partial differential equations.
02.50.Ey - Stochastic processes.
02.70.Uu - Applications of Monte Carlo methods.
89.65.Gh - Economics; econophysics, financial markets, business and management .
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2004