This article reports on the contents of a tutorial session at MCQMC 2008. The tutorial explored various places in statistics where Monte Carlo methods can be used. There was a special emphasis on areas where Quasi-Monte Carlo ideas have been or could be applied, as well as areas that look like they need more research.

The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The aim of this review ...

Quasi-Monte Carlo is usually employed to speed up the convergence of Monte Carlo in approximating multivariate integrals. While convergence of the Monte Carlo method is O(N−1/2), that of plain quasi-Monte Carlo can achieve O(N−1). Several methods exist to increase its convergence to O(N−α ), α > 1, if the integrand has enough smoothness. We discuss two methods: lattice rules with periodization ...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, which we proposed in an earlier paper [32], to the evaluation of an European Call option and of an Asian Call option. We assume that the stock price of the underlying asset S = S(t) is driven by a Lévy process Z(t), with independent increments distributed according to a NIG distribution. We compare our method with the ...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, developed by us in a previous paper [31], to the evaluation of barrier options. We assume that the stock price of the underlying asset is driven by a Lévy process with independent increments distributed according to a NIG distribution. We also provide numerical results that compare our method with the Monte Carlo metho...

In recent years, the quasi-Monte Carlo approach for pricing high-dimensional derivative securities has been used widely relative to other competitive approaches such as the Monte Carlo methods. Such success can be, in part, attributed to the notion of effective dimension of the finance problems. In this paper, we provide additional insight on the connection between the effective dimension and t...

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account ...

Monte Carlo methods are frequently used for neutron and radiation transport. These methods have several advantages, such as relative ease of programming and dealing with complex meshes. Disadvantages include long run times and statistical noise. Monte Carlo photon transport calculations also often suffer from inaccuracies in matter temperature due to the lack of implicitness. In this paper we d...

Options is an important financial derivative products, therefore it is important to reasonable pricing. According to the financial asset returns typically exhibit the feature of aiguilles large remaining part and hypothesis, it obeys normal inverse Gaussian distribution, using Monte Carlo simulation based on normal inverse Gaussian distribution on its pricing and improving it by antithesis vari...

This paper suggests a bootstrap testing procedure for determining the rank of cointegrated systems. The properties of the new testing procedure are investigated using Monte Carlo techniques. The performance of the test compares favourably to that of the widely used procedures for determining cointegration rank proposed by Johansen (1988). JEL classi cation: C12; C15; C32.