Monte Carlo EM methods and Particle approximations: Application to the calibration of a stochastic volatility model.
type: Dataset
contact point: Organization
  fn: CCSD
keyword: higher-order-markov-chain
keyword: mcem
keyword: stochastic-volatility-model
keyword: modeles-de-markov-caches
keyword: chaine-de-markov-dorde-superieur
keyword: infoinfo-mocomputer-science-csmodeling-and-simulation
keyword: methodes-monte-carlo-sequentielles
keyword: theses
keyword: hidden-markov-models
keyword: sequential-monte-carlo-methods
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: modele-de-volatilite-stochastique
keyword: infoeu-reposemanticsdoctoralthesis
landing page: https://theses.hal.science/tel-00942243
description: This thesis pursues a double perspective in the joint use of sequential Monte Carlo methods (SMC) and the Expectation-Maximization algorithm (EM) under hidden Markov models having a Markov dependence structure of order grater than one in the unobserved component signal. Firstly, we begin with a brief description of the theoretical basis of both statistical concepts through Chapters 1 and 2 that are devoted. In a second hand, we focus on the simultaneous implementation of both concepts in Chapter 3 in the usual setting where the dependence structure is of order 1.The contribution of SMC methods in this work lies in their ability to effectively approximate any bounded conditional functional in particular, those of filtering and smoothing quantities in a non-linear and non-Gaussian settings. The EM algorithm is itself motivated by the presence of both observable and unobservable (or partially observed) variables in Hidden Markov Models and particularly the stochastic volatility models in study. Having presented the EM algorithm as well as the SMC methods and some of their properties in Chapters 1 and 2 respectively, we illustrate these two statistical tools through the calibration of a stochastic volatility model. This application is done for exchange rates and for some stock indexes in Chapter 3. We conclude this chapter on a slight departure from canonical stochastic volatility model as well Monte Carlo simulations on the resulting model.Finally, we strive in Chapters 4 and 5 to provide the theoretical and practical foundation of sequential Monte Carlo methods extension including particle filtering and smoothing when the Markov structure is more pronounced. As an illustration, we give the example of a degenerate stochastic volatility model whose approximation has such a dependence property.
issued: 2026-05-07T02:47:21.095563
language: fr
modified: 2026-05-07T02:47:21.095568

Monte Carlo EM methods and Particle approximations: Application to the calibration of a stochastic volatility model.
type: Distribution
access URL: https://theses.hal.science/tel-00942243
format: HTML
issued: 2026-05-07T02:47:21.105382
modified: 2026-05-07T02:47:21.081953

test_moissonnage_selune
type: Agent