arXiv research

A new scheme for FBSDEs simplifies computation without Monte Carlo.

Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…

In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order $1/2$. This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined ad…

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo me…

GPU speeds up Monte Carlo simulations for large time steps.

We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the finance problem under consideration require e.g. continuous monitoring of the pro…

New symplectic scheme speeds up RMHMC.

New method for sampling orthogonal matrices using Hamiltonian Monte-Carlo.

Compressed Monte Carlo improves efficiency in Bayesian inference.

Improved sampling for network community detection.

Deep learning accelerates Monte Carlo SDE simulations with large time steps.

A fast Monte Carlo method for additive processes and option pricing.

Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.

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…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performan…

Improved multilevel scheme for value-at-risk computation.

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be …

New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.

Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…

New bounds for SMC show its advantage over MCMC in multimodal distributions.

Improves MCMC performance with adaptive affine transformations.

New method uses symmetric splitting for efficient HMC inference in large neural networks.

Generative models map simple samples to complex target samples.

CHMC improves HMC efficiency for multimodal distributions.

Paper shows strong convergence rates for fractional processes using Ornstein-Uhlenbeck representations.

We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at $m$ fixed dates. Our approach yields unbiased estimators with standard deviation $O(ε)$ in $O(m + (1/ε)^{2})$ expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…

A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.

AES scheme improves Bermudan and American option pricing for Heston models.

Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such a Monte Carlo scheme which converges to the exact value. We manage to keep the s…

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotr…

Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.

New method improves training-free guidance for diffusion models, achieving state-of-the-art results.

A new method improves graph random features with quasi-Monte Carlo techniques.

Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some…

In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…

There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for w…

New method improves sampling efficiency in complex stochastic systems.

Adaptive quadrature improves Bayesian inference through active learning.

Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…

New method for pricing discrete Asian and Lookback options under Heston model.

Gradient learning optimises MCMC proposal distributions.

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the continuous diffusion process associated with the algorithm converges exponentially fa…

Novel numerical scheme for G-heat equation with uncertainty.

Deep learning improves option pricing for a non-martingale asset model.

This survey explores various optimality concepts in importance sampling.

MCFlow uses Monte Carlo sampling and flow models for imputing missing data.

The paper extends Hamiltonian Monte Carlo to Lie groups and constrained mechanics.