We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [J.P. Fouque, G. Papanicolaou, R. Sircar and K. Solna: Multiscale Stochastic Volatility Asymptotics, SIAM Journal on Multiscale Modeling a...

Quasi-Monte Carlo (QMC) methods are playing an increasingly important role in the pricing of complex financial derivatives. For models in which the prices of the underlying assets are driven by Brownian motions, the efficiency of QMC methods is known to depend crucially on the method of generating the Brownian motions. This paper focuses on the impact of various constructions. While the Brownia...

In this paper we present an FPGA implementation of a Monte-Carlo method for pricing Asian Options using Impulse C and floating-point arithmetic. In an Altera Stratix-V FPGA, a 149x speedup factor was obtained against an OpenMP-based solution in a 4-core Intel Core i7 processor. This speedup is comparable to that reported in the literature using a classic HDL-based methodology, but the developme...

We propose a fast and stable numerical method to evaluate two-dimensional partial differential equation (PDE) for pricing arithmetic average Asian options. The numerical method is deduced by combining an alternating-direction technique and the central difference scheme on a piecewise uniform mesh. The numerical scheme is stable in the maximum norm, which is true for arbitrary volatility and arb...

This paper studies the ANOVA decomposition of a d-variate function f defined on the whole of Rd, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions all terms of the ANOVA decomposition, except the one of highest order, can have unlimited smoothness...