All the results of the preceding lecture show that the ratio σ/ √ N governs the accuracy of a Monte-Carlo method with N simulations. An obvious consequence of this fact is that one always has interest to rewrite the quantity to compute as the expectation of a random variable which has a smaller variance : this is the basic idea of variance reduction techniques. For complements, we refer the rea...

We investigate the setting in which Monte Carlo methods are used and draw a parallel to the formal setting of statistical inference. In particular, we nd that Monte Carlo approximation gives rise to a bias-variance dilemma. We show that it is possible to construct a biased approximation schemes with a lower approximation error than a related unbiased algorithms.

McKay, Conover and Beckman (1979) introduced Latin hypercube sampling (LHS) for reducing variance of Monte Carlo simulations. More recently Owen (1992a) and Tang (1993) generalized LHS using orthogonal arrays. In the Owen's class of generalized LHS, we de ne extended Latin hypercube sampling of strengthm (henceforth denoted as ELHS(m)), such that ELHS(1) reduces to LHS. We rst derive explicit f...

We developed a new scheme for computing ”Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asympt...

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are give...

An analytical evaluation of the thyroid stimulating hormone (TSH-3) assay on the Bayer ADVIA Centaur immunoassay system was performed. General analytical requirements (linearity, resistance to typical interferences, absence of a carry-over effect) were fulfilled and reproducibility was satisfactory. Inter-assay coefficient of variation (CV) of a human serum pool with a concentration of 0.014 mU...

Many fields require computing the trace of the inverse of a large, sparse matrix. Since dense matrix methods are not practical, the typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its slow convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of defl...

there have been several efforts in the literature to extract as much information as possible from the financial networks. most of the research has been concerned about the hierarchical structures, clustering, topology and also the behavior of the market network; but not a notable work on the network filtration exists. this paper proposes a stock market filtering model using the correlation - ba...