GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from parallel implementations, and consequently Monte Carlo has become a focal point …
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48 results for “randomized quasi-Monte Carlo”
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no pa…
A new method improves graph random features with quasi-Monte Carlo techniques.
problem Improving the accuracy of graph random features.
method Induces negative correlations in random walks using antithetic termination.
result Strong theoretical guarantees on lower-variance estimators of the Laplacian kernel.
Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.
problem Improving the efficiency of numerical integration methods.
method Uses normalizing flows to approximate distributions and quasi-Monte Carlo for sampling.
result Demonstrates an estimator with significantly lower variance.
RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.
problem Improving kernel-based learning methods to reduce deterministic error and computational complexity.
method Randomized quasi-Monte Carlo (RQMC) methods applied to random feature approximations.
result RQMC methods improve deterministic approximation error bound from to , matching QMC methods.
RQMC improves QMC by providing practical error bounds for financial applications.
problem Lack of practical error estimates in QMC methods.
method Combines Sobol LDS with randomized scrambling methods.
result RQMC outperforms standard QMC in convergence rates and provides error bounds.
Repelling Random Walksstat.ML
Repelling random walks improve graph-based sampling efficiency.
problem Efficient graph-based sampling and statistical estimation.
method Induces correlations between trajectories of an ensemble of walkers on a graph, maintaining unbiasedness.
result Improves concentration of statistical estimators on graphs.
Comparative Study of Monte Carlo and Quasi-Monte Carlo Techniques for Enhanced Derivative Pricingq-fin.PR
This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.
problem Improving derivative pricing accuracy and efficiency in high-dimensional settings.
method Compared Monte Carlo and quasi-Monte Carlo techniques, focusing on convergence rates and low-discrepancy sequences.
result Quasi-Monte Carlo methods achieve superior convergence rates and reduce root mean square error in derivative pricing.
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p…
RQMC improves optimization in variational Bayes problems.
problem Optimizing variational Bayes problems with noisy objective functions.
method Use of randomized quasi-Monte Carlo (RQMC) sampling with stochastic L-BFGS.
result RQMC can significantly speed up optimization and find better parameter values.
Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.
problem Estimating Greeks for barrier and arithmetic average Asian options.
method Global sensitivity analysis, Chebyshev interpolation, conditional pathwise method, randomized Quasi Monte Carlo, Brownian bridge discretization, importance sampling.
result Reduced effective dimensionality enhances convergence rate and accuracy of randomized Quasi Monte Carlo integration.
Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure to obtain adaptive quadrature rules for integrals of functions in a reproducing kernel Hilbert space (RKHS) with a potentially faster rate of convergence than Monte Carlo integration (and "kernel herding" was shown to be a special case of thi…
Proposes QMC-based QSW for 3D SW distance.
problem Intractable SW distance in 3D.
method Quasi-Monte Carlo (QMC) for QSW approximations.
result QMC-based QSW improves SW estimation.
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…
Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.
problem Derivative pricing and risk analysis in a hyperbolic local volatility model.
method Application of Monte Carlo and Quasi Monte Carlo methods for pricing and risk analysis.
result Quasi Monte Carlo methods show superior performance in high-dimensional integration for derivative pricing and risk analysis.
This thesis advances algorithms and software for QMC, GP, and sciML.
problem Efficient high-dimensional integration, interpolation, and PDE modeling.
method Developed new algorithms and software for QMC, GP, and sciML.
result Efficient and accurate methods for high-dimensional problems.
One of the main practical applications of quasi-Monte Carlo (QMC) methods is the valuation of financial derivatives. We aim to give a short introduction into option pricing and show how it is facilitated using QMC. We give some practical examples for illustration.
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo (QMC) sam…
Quasi-Monte Carlo speeds up option Greeks calculation on GPUs.
problem Efficiently calculating option Greeks for risk management.
method Quasi-Monte Carlo (QMC) combined with GPU acceleration for pathwise sensitivity calculation.
result Increased computational speed and efficiency in estimating option Greeks.
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
problem Computing the integral of a function on the unit sphere using Monte Carlo methods.
method The approach involves using determinantal point processes and repelled point processes to create quadratures for the sliced Wasserstein distance.
result The UnifOrtho estimator is recommended for the computation of the sliced Wasserstein distance in large dimensions.
Corrects errors in ILA for Bayesian inference in LGMs.
problem Error in ILA for non-Gaussian likelihoods in LGMs.
method Importance sampling scheme to correct ILA errors.
result Corrected posterior converges to the true posterior with increased samples.
New method reduces variance in estimating PL model expectations.
problem High variance in Monte Carlo estimates of PL model expectations.
method Combining Gumbel top-k trick with quasi-Monte Carlo sampling.
result More sample-efficient estimators of PL model expectations.
Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC) integration [Yang …
Transport Quasi-Monte Carlomath.NA
Improves QMC for complex distributions using transport maps.
problem Challenges in applying QMC to general target distributions.
method Train a transport map to approximate target distributions, ensuring RQMC achieves superior error rates.
result Transport QMC achieves faster convergence rates than standard Monte Carlo under mild conditions.
Langevin Quasi-Monte Carlostat.CO
LMC improves sampling from complex distributions using quasi-random sequences.
problem Sampling from complex high-dimensional distributions with high accuracy.
method Using completely uniformly distributed (CUD) sequences in Langevin Monte Carlo (LMC) to generate Gaussian perturbations.
result LMC with low-discrepancy CUD sequences achieves smaller estimation error than standard LMC.
Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeksq-fin.CP
QMC and GSA improve option pricing and risk measures efficiency.
problem Efficiently pricing and hedging complex financial instruments.
method Application of QMC and GSA techniques for financial instrument pricing and hedging, comparing MC vs QMC and analyzing greeks computation.
result QMC outperforms MC in most cases, especially in high-dimensional simulations, leading to faster and more stable convergence.
A new method slices and sums radial kernels faster.
problem Fast computation of large kernel sums in kernel methods.
method Random projections to 1D subspaces and QMC for selecting projections.
result QMC-slicing outperforms existing methods on test datasets.
This study compares MC and QMC methods for likelihood functions.
problem Approximating the normalizing constant of posterior distributions and marginal likelihoods.
method Characterizes the integration error of MC and QMC methods for likelihood functions.
result QMC outperforms MC under certain conditions, especially in high dimensions.
New sampling methods improve Shapley value estimation for machine learning models.
problem Approximating Shapley values for non-trivial models is computationally challenging.
method Investigates new quadrature techniques and quasi-Monte Carlo methods for permutation sampling.
result Significant improvements in Shapley value estimates over existing methods.
Sensitivity Analysis on Policy-Augmented Graphical Hybrid Models with Shapley Value Estimationstat.ML
Framework for sensitivity analysis in biomanufacturing processes.
problem High complexity and uncertainty in biomanufacturing processes.
method Shapley value estimation for linear and nonlinear pKG models, using quasi-Monte Carlo and antithetic sampling.
result Improved efficiency and accuracy in sensitivity analysis for biomanufacturing processes.
Paper improves Monte Carlo sampling with new theoretical insights and methods.
problem Improving Monte Carlo sampling for variance reduction.
method Theoretical analysis of negatively dependent random variables and novel extensions using number theory and particle algorithms.
result Near-Orthogonal Monte Carlo (NOMC) consistently outperforms Orthogonal Monte Carlo (OMC) in various applications.
Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysisq-fin.RM
We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequen…
New method smooths integrands for efficient option pricing.
problem Improving numerical performance of option pricing methods.
method Combining hierarchical adaptive sparse grids, quasi-Monte Carlo, and numerical smoothing.
result Improved efficiency of ASGQ and QMC methods for high-dimensional problems.
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl…
This paper discusses the exact simulation of the stock price process underlying the 3/2 model. Using a result derived by Craddock and Lennox using Lie Symmetry Analysis, we adapt the Broadie-Kaya algorithm for the simulation of affine processes to the 3/2 model. We also discuss variance reduction techniques and find th…
Exciton diffusion plays a vital role in the function of many organic semiconducting opto-electronic devices, where an accurate description requires precise control of heterojunctions. This poses a challenging problem because the parameterization of heterojunctions in high-dimensional random space is far beyond the capa…
We approximate differential entropy for efficient Bayesian experimental design.
problem Efficiently estimating expected information gain in large-scale inference problems.
method Approximate differential entropy using Monte Carlo or quasi-Monte Carlo surrogates.
result Our approach achieves comparable or better convergence rates than state-of-the-art methods.
Quasi-Monte Carlo with Domain Transformation for Efficient Fourier Pricing of Multi-Asset Optionsq-fin.CP
This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.
problem Efficiently pricing multi-asset options in high dimensions with Fourier methods.
method Randomized quasi-Monte Carlo (RQMC) with domain transformation to handle singularities.
result RQMC with domain transformation provides accurate and scalable Fourier pricing for multi-asset options.
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error. Bayesian optimization is a promising technique for efficiently optimizing multi…
The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied volatility surfaces. In the absence of analytical European option pricing methods f…
We improve Gaussian copula models for imputing mixed data types with precise approximations.
problem Imputing missing values with mixed data types in surveys and medical applications.
method We use randomized quasi-Monte Carlo procedures for direct and arbitrarily precise approximations of model estimation and imputation.
result Our method yields lower errors for model parameters and imputed values compared to existing methods.
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and…
Generative moment matching networks (GMMNs) are introduced for generating quasi-random samples from multivariate models with any underlying copula in order to compute estimates under variance reduction. So far, quasi-random sampling for multivariate distributions required a careful design, exploiting specific propertie…
Efficiently reduces computational burden of rollout acquisition functions in Bayesian optimization.
problem Expensive computation of rollout acquisition functions in Bayesian optimization.
method Combines quasi-Monte Carlo, common random numbers, and control variates to reduce computational burden. Formulates a policy-search approach to eliminate the need to optimize the rollout acquisition function.
result Significant reduction in computational burden of rollout acquisition functions.
Deep learning observables in computational fluid dynamicsphysics.comp-ph
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large number of expensive (forward) numerical solutions of the corresponding PDEs. We pro…
AGMMNs improve learning of copula models by adaptively selecting kernels.
problem Learning dependence structures in copula models.
method Adaptive bandwidth selection for MMD in GMMNs, increasing kernels based on validation loss.
result AGMMNs significantly improve training performance over GMMNs and parametric models.
Data compression speeds up machine learning loss calculations.
problem Computational demand in calculating mean squared error for large datasets.
method Use rank-1 lattices to compress data, assigning weights based on original data and responses.
result Our QMC data compression algorithms can lead to arbitrary high convergence rates for smooth functions.
LSH methods extend to function spaces for efficient similarity search.
problem Efficient similarity search in function spaces.
method Locality-sensitive hashing (LSH) extended to spaces using function approximation or Monte Carlo techniques.
result An LSH family for Wasserstein distance over continuous probability distributions.