Séminaire Statistique
organisé par l'équipe Statistique
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Éléonore Blanchard
Approximate Bayesian Calibration of Option Pricing Models
7 février 2025 - 11:00Salle de séminaires IRMA
Nous proposons une méthodologie pour la calibration de modèles financiers complexes basée sur l'algorithme Approximate Bayesian Computation (ABC). Cette approche permet de calibrer les paramètres de modèles nécessitant un pricing par Monte-Carlo. Nous appliquons la méthodologie à un modèle exponentiel de Levy et un modèle exponentiel de Levy modulé par une chaîne de Markov. Nos expériences, réalisées sur données simulées et réelles (options européennes sur le S&P500), montrent que l'algorithme ABC fournit des calibrations précises. En complément, une approche par processus gaussiens améliore la stabilité des calibrations dans le temps. Cette étude démontre l'efficacité et la flexibilité d'ABC pour la calibration de modèles complexes, ouvrant des perspectives pour son application à des produits dérivés plus sophistiqués. -
Hidden Markov Models (HMMs) are powerful tools for modeling time-dependent phenomena governed by underlying dynamic processes that are only partially observable. However, standard estimation techniques for HMMs — such as maximum likelihood, least square and spectral methods — often suffer from sensitivity to model misspecification, outliers, and data contami- nation, resulting in unreliable parameter estimates. To overcome these challenges, we introduce a novel estimation method based on ρ-estimators, a class of robust estimators developed by Baraud et al. [1, 2] for independent set- tings. We prove a non-asymptotic bound on the Hellinger distance between the target distribution and our estimator. It allows us to derive a minimax convergence rate (up to a logarithmic factor) in the well-specified case. We establish the robustness of the estimator by demonstrating that its performance remains stable under contamination, as long as the contamination rate is moderate, regardless of the type of contamination. We can notice a posteriori that the proposed method is not restricted to HMMs and can be generalized to other models satisfying similar properties. For instance, we obtain results for the estimation of the stationary distribution for a class of Langevin diffusions.
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Yiye Jiang
Graph learning from time series in complex data settings
7 mars 2025 - 11:00Salle de séminaires IRMA
Graph learning is an active research domain in statistics, highlighted by well-known models such as Gaussian graphical models for i.i.d. data and autoregressive models for time series. In this talk, we will present two new models developed to address distinct analytical challenges. The first model tackles a non-classical data setting where the data points are probability distributions. Here, the graph is inferred to represent the dependence structure of a set of distributional time series. Leveraging Wasserstein space theory, we develop a novel autoregressive model, which is then applied to a demographic dataset. The second model is designed to meet an application-driven need: inferring a functional connectivity graph for a single subject’s brain fMRI time series while quantifying uncertainty. We adopt a Bayesian modeling approach to infer these graphs, with posterior distributions over edges providing uncertainty estimates. In particular, we introduce a prior for correlation matrices that facilitates the integration of expert knowledge. The model is applied to a rat fMRI dataset, where two follow-up analyses—edge detection and subject comparison—are conducted. The results highlight the robustness gained through uncertainty quantification.