This article discusses the general problem of generating representative point sets from a distribution known up to a multiplicative constant. The sampling/importance resampling (SIR) algorithm is known to be useful in this context. Moreover, the quasi-random sampling/importance resampling (QSIR)...

The standard domain for quasi-Monte Carlo approximations is the unit cube. Recently, much research has been done to make quasi-Monte Carlo methods applicable to the real space. Mathé and Wei proposed an algorithm that splits Rd into cubes. One of the difficulties with their approach is that the...

The Faure sequence is one of the well-known quasi-random sequences used in quasi-Monte Carlo applications. In its original and most basic form, the Faure sequence suffers from correlations between different dimensions. These correlations result in poorly distributed two-dimensional projections....

We consider the integral of a function and its approximation by a quadrature rule of the form i.e. by a rule which uses the values of both and its derivative at nodes of the quadrature rule. We examine the cases when the integrand is either a smooth function or an dependent function of the form...

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance...

We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the...