Cyrille DUBARRY

PhD thesis

Cyrille DUBARRY — 2012-05-09T13:53:18Z

Smoothing and estimation methods in hidden variable models through sequential Monte-Carlo methods.

- Research

Project : Gaussian mixture

Cyrille DUBARRY — 2010-04-19T21:17:10Z

The following document is in French. See the French article for more details.

Stochastic modeling and simulation

Cyrille DUBARRY — 2010-04-19T21:01:42Z

The following documents are in French. See the French article for more details.

Online options pricer

Cyrille DUBARRY — 2010-04-12T21:17:46Z

When we were students from the Mathematical Finance curriculum at Télécom ParisTech, Raphaël Bensoussan, Paul Jouguet and myself made on online options pricer website. It was conceived within the framework of a free project, managed by Laurent Decreusefond.

You can click here to access the website.

Monte-Carlo methods applied to finance

Cyrille DUBARRY — 2010-04-11T18:04:19Z

The following documents are in French. See the French article for more details.

Stochastic calculus applied to finance

Cyrille DUBARRY — 2010-04-11T17:52:12Z

The following documents are in French. See the French article for more details.

On the convergence of Island particle models

Cyrille DUBARRY — 1969-12-31T23:59:59Z

- International Journals

Particle approximation improvement of the joint smoothing distribution with on-the-fly variance estimation.

Cyrille DUBARRY — 1969-12-31T23:59:59Z

Particle smoothers are widely used algori\-thms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve any of them with a linear complexity in the number of particles. When iteratively applied to the degenerated Filter-Smoother, this method leads to an algorithm which turns out to outperform existing linear particle smoothers for a fixed computational time. Moreover, the associated approximation satisfies a central limit theorem with a close-to-optimal asymptotic variance, which can be easily estimated by only one run of the algorithm. This last feature is totally new in the smoothing literature.

Key words: Degeneracy, Hidden Markov model, Particle smoothing, Sequential Monte-Carlo, Variance estimation

Calibrating the exponential Ornstein-Uhlenbeck multiscale stochastic volatility model

Cyrille DUBARRY — 1969-12-31T23:59:59Z

This paper exhibits a tractable and efficient way of calibrating a multiscale exponential Ornstein-Uhlenbeck stochastic volatility model including a correlation between the asset and its volatility. As opposed to many contributions where this correlation is assumed to be null, this framework allows to describe the leverage effect widely observed in equity markets. The resulting model is non exponential and driven by a degenerated noise, thus requiring high carefulness about the estimation algorithm design. The way we overcome this difficulty provides guidelines concerning the development of estimation algorithm in non standard framework. We propose to use a block-type expectation maximization algorithm along with particle smoothing. This method results in an accurate calibration process able to identify up to three time scale factors. Furthermore, we introduce an intuitive heuristic which can be used to choose the number of factors.

Key words: Multiscale stochastic volatility model, Inference, Particle smoothing, Maximum split data estimate, EM algorithm (Expectation-maximization)

Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models.

Cyrille DUBARRY — 1969-12-31T23:59:59Z

The approximation of fixed-interval smoothing distributions is a key issue in inference for general state-space hidden Markov models (HMM). This contribution establishes non-asymptotic bounds for the Forward Filtering Backward Smoothing (FFBS) and the Forward Filtering Backward Simulation (FFBSi) estimators of fixed-interval smoothing functionals. We show that the rate of convergence of the -mean errors of both methods depends on the number of observations and the number of particles only through the ratio T/N for additive functionals. In the case of the FFBS, this improves recent results providing bounds depending on T/\sqrt{N}.

Key words: Additive functionals, Deviation inequalities, FFBS, FFBSi, Particle-based approximations, Sequential Monte Carlo methods (SMC)