Over-parameterisation is a key issue in (integrated) environmental modelling. Therefore, a sensitivity analysis (SA) can assist in the proper application of a complex environmental model, such as the Soil and Water Assessment Tool (SWAT). A very powerful sensitivity analysis technique that is gaining popularity in environmental modelling is the variance-based Sobol’ method. Still, the high numb...

A method for generating sequences of quasirandom numbers allows conventional serial Monte Carlo algorithms to be parallelized with no loss of computation eeciency. Speciically, a Sobol' sequence can be broken up into interleaved subsets; with each processing node calculating a unique subset of the full sequence, all of the computational advantages of quasirandom Monte Carlo methods over pure-ra...

The Soból sequence is the most popular quasirandom sequence because of its simplicity and efficiency in implementation. We summarize aspects of the scrambling technique applied to Soból sequences and propose a new simpler modified scrambling algorithm, called the multi-digit scrambling scheme. Most proposed scrambling methods randomize a single digit at each iteration. In contrast, our multi-di...

We introduce a class of functions in d ≥ 3 dimensions which have arbitrary odd superposition effective dimensions between three and d inclusive. We prove that for the integration of any function in this class any Sobol’ points of a fixed length have zero error, whereas Owen’s scrambling of any Sobol’ points of the same length has the same variance of error as simple Monte Carlo methods. Further...

In the context of multi-factor stochastic volatility models, which contain the widely used Heston model, we present variance reduction techniques to price European options by Monte Carlo (MC) and QuasiMonte Carlo (QMC) methods. We formulate a stochastic integral as a martingale control for the payoffs to be evaluated. That control corresponds to the cost of an approximate delta hedging strategy...

Fitting a probability distribution to observed or generated data constitutes an essential part of any data analysis system. The Generalized Lambda Distribution, while extremely versatile in this regard, is also a difficult distribution to fit. Parameter estimation methods that attempt to match moments or quantiles of the data require minimizing a bivariate non-linear function. The suitability o...

In this paper we study the possibility to use the Sobol’ and Halton quasi-random number sequences (QRNs) in solving the BarkerFerry (B-F) equation which accounts for the quantum character of the electron-phonon interaction in semiconductors. The quasi-Monte Carlo (QMC) solutions obtained by QRNs are compared with the Monte Carlo (MC) solutions in case when the scalable parallel random number ge...

In this paper we show that it is possible to extend the use of quasi-Monte Carlo for applications of high effective dimension. This is achieved through a combination of a careful construction of the Sobol sequence and an appropriately chosen decomposition of a covariance matrix. The effectiveness of this procedure is demonstrated as we price average options with nominal dimensions ranging up to...