Variance reduction by antithetic random numbers of Monte Carlo methods for unrestricted and reflecting diffusions

C. Costantini

Mathematics and Computers in Simulation (MATCOM), 1999, vol. 51, issue 1, 1-17

Abstract: The main discretization schemes for diffusion processes, both unrestricted and reflecting in a hyper-rectangle, are considered. For every discretized path, an `antithetic' path is obtained by changing the sign of the driving random variables, which are chosen symmetric. It is shown that, under suitable monotonicity assumptions on the coefficients and boundary data, the mean of a sample of values of a monotone functional evaluated on M independent discretized paths and on the M corresponding antithetic paths has a smaller variance than the mean of a sample of values of the same functional evaluated on 2M independent paths. An example, obtained by reflecting the diffusion process of the well-known Black and Scholes model of finance, is discussed. The results of some numerical tests are also presented.

Keywords: Variance reduction; Simulation; Stochastic differential equations; Boundary conditions (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475499000944
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:51:y:1999:i:1:p:1-17

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().