The Library

An empirical study of the efficiency of EA for diffusion simulation

Tools

Peluchetti, Stefano and Roberts, Gareth O. (2008) An empirical study of the efficiency of EA for diffusion simulation. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2008 (No.14).

Preview

PDF
WRAP_Pelcuhetti_08-14w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (8Mb)

Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

In this paper we investigate the efficiency of some simulation schemes for the
numerical solution of a one dimensional stochastic differential equation (SDE). The schemes
considered are: the Exact Algorithm (EA), the Euler, the Predictor-Corrector and the Ozaki-
Shoji schemes. The focus of the work is on EA which samples skeletons of SDEs without
any approximation. The analysis is carried out via a simulation study using some test SDEs.
We also consider efficiency issues arising by the extension of EA to the multi-dimensional
setting.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Stochastic differential equations, Diffusion processes

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2008

Dates:

Date	Event
2008	Published

Volume:

Vol.2008

Number:

No.14

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

References:

Y. Ait-Sahalia. Closed-Form Likelihood Expansions for Multivariate Diffusions. 2002.
C. Albanese and A. Kuznetsov. Transformations of Markov processes and classification scheme for solvable driftless diffusions. preprint, www3. imperial. ac.
uk/mathfin/people/calban/papersmathfin, 2005.
A. Beskos and G.O. Roberts. Exact simulation of diffusions. Ann. Appl. Probab, 15:2422-
2444, 2005.
A. Beskos, O. Papaspiliopoulos, and G.O. Roberts. Retrospective exact simulation of diffusion
sample paths with applications. Bernoulli, 12:1077-1098, 2006a.
A. Beskos, O. Papaspiliopoulos, and G.O. Roberts. A new factorisation of diffusion measure
and finite sample path construction. Methodology and Computing in Applied Probability,
Submitted, 2006b.
Bruno Casella. Exact MC simulation for diffusion and jump-diffusion processes with financial
applications. PhD thesis, IMQ - Bocconi University, 2005.
WR Gilks. Derivative-free adaptive rejection sampling for Gibbs sampling. Bayesian Statis-
tics, 4(2):641-649, 1992.
WR Gilks and P. Wild. Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics,
41(2):337-348, 1992.
P.E. Kloeden and E. Platen. Numerical Solution of Stochastic Differential Equations.
Springer, 1992.
G. Maruyama. Continuous markov processes and stochastic equations. Rend. Circ. Mat.
Palermo, 4:48-90, 1955.
Stefano Peluchetti. An analysis of the efficiency of the Exact Algorithm. PhD thesis, IMQ -
Universitá Commerciale Luigi Bocconi, 2007.
I. Shoji and T. Ozaki. Estimation for nonlinear stochastic differential equations by a local
linearization method. Stochastic Analysis and Applications, 16(4):733-752, 1998.