Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
MATHEMATICS OF COMPUTATION Volume 00, Number 0, Pages 000{000
 

Summary: MATHEMATICS OF COMPUTATION
Volume 00, Number 0, Pages 000{000
S 0025-5718(XX)0000-0
[]
A PARTIAL DIFFERENTIAL EQUATION CONNECTED TO
OPTION PRICING WITH STOCHASTIC VOLATILITY:
REGULARITY RESULTS AND DISCRETIZATION
YVES ACHDOU, BRUNO FRANCHI, AND NICOLETTA TCHOU
Abstract. This paper completes a previous work [1] on a Black and Scholes
equation with stochastic volatility. This is a degenerate parabolic equation,
which gives the price of a European option as a function of the time, of the
price of the underlying asset and of the volatility, when the volatility is a
function of a mean reverting Orstein-Uhlenbeck process, possibly correlated
with the underlying asset. The analysis involves weighted Sobolev spaces. We
give a characterization of the domain of the operator, which permits to use
results from the theory of semi-groups. We then study a related model elliptic
problem and we propose a nite element method with a regular mesh with
respect to the intrinsic metric associated with the degenerate operator. For
the error estimate, we need to prove an approximation result.
1. Introduction

  

Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Mathematics