Peluchetti, Stefano and Roberts, Gareth O. (2008) An empirical study of the efficiency of EA for diffusion simulation. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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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
Date:	2008
Volume:	Vol.2008
Number:	No.14
Number of Pages:	26
Status:	Not Peer Reviewed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.
URI:	http://wrap.warwick.ac.uk/id/eprint/35489

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