ArrayRQMC for option pricing under stochastic volatility models ArrayRQMC has been proposed as a way to effectively apply randomized quasiMonte Carlo (RQMC) when simulating a Markov chain over a large number of steps to estimate an expected cost or reward. The method can be very effective when the state of the chain has low dimension. For pricing an Asian option under an ordinary geometric Brownian motion model, for example, ArrayRQMC reduces the variance by huge factors. In this paper, we show how to apply this method and we study its effectiveness in case the underlying process has stochastic volatility. We show that ArrayRQMC can also work very well for these models, even if it requires RQMC points in larger dimension. We examine in particular the variancegamma, Heston, and OrnsteinUhlenbeck stochastic volatility models, and we provide numerical results.

Efficient Stochastic Approaches for Multidimensional Integrals in Bayesian Statistics A fundamental problem in Bayesian statistics is the accurate evaluation of multidimensional integrals. A comprehensive experimental study of quasiMonte Carlo algorithms based on Sobol sequence combined with Matousek linear scrambling and a comparison with adaptive Monte Carlo approach and a lattice rule based on generalized Fibonacci numbers has been presented. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing high dimensional integrals. It is a crucial element since this may be important to be estimated in order to achieve a more accurate and reliable interpretation of the results in Bayesian statistics which is foundational in applications such as machine learning.