Related papers: Sequential Monte Carlo Methods for Option Pricing
In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a fast sequential design algorithm for these models relative to the…
We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…
An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…
In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…
Array-RQMC has been proposed as a way to effectively apply randomized quasi-Monte 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…
The shell model Monte Carlo (SMMC) method is a powerful technique for calculating the statistical and collective properties of nuclei in the presence of correlations in model spaces that are many orders of magnitude larger than those that…
This paper focus on pricing exchange option based on copulas by MCMC algorithm. Initially, we introduce the methodologies concerned about risk-netural pricing, copulas and MCMC algorithm. After the basic knowledge, we compare the option…
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an…