Publication
Title
Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
Author
Abstract
 Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.
Language
English
Source (journal)
European physical journal : B : condensed matter and complex systems. - Berlin
Publication
Berlin : 2010
ISSN
1434-6028 [print]
1434-6036 [online]
Volume/pages
75 :3 (2010) , p. 335-342
ISI
000278473500009
Full text (Publisher's DOI)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address