Papers by Jean-David Fermanian
Canadian Journal of Statistics
Several procedures have been recently proposed to test the simplifying assumption for conditional... more Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general borelian conditioning subsets. Several test statistics based on the equality of conditional Kendall's tau are introduced, and we derive their asymptotic distributions under the null. When such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. It is based on decision trees that maximize the differences between the conditional Kendall's taus corresponding to the leaves of the trees. The performances of such tests are illustrated in a simulation experiment. Moreover, a study of the conditional dependence between financial stock returns is managed, given some clustering of their past values. The last application deals with the conditional dependence between coverage amounts in an insurance dataset.
arXiv (Cornell University), Mar 6, 2012
We propose a new platform of goodness-of-fit tests for copulas, based on empirical copula process... more We propose a new platform of goodness-of-fit tests for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based on the empirical copula process indexed by families of L n disjoint boxes, with L n slowly tending to infinity. Although the underlying empirical process does not converge, the critical values of our new test statistics can be consistently estimated by nonparametric bootstrap techniques, under simple or composite null assumptions. We implemented a particular example of these tests and our simulations confirm that the power of the new procedure is oftentimes higher than the power of the standard Kolmogorov-Smirnov or the Cramér-von Mises tests for copulas.
arXiv (Cornell University), Dec 22, 2021
We study the large sample properties of sparse M-estimators in the presence of pseudo-observation... more We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their empirical counterparts. It is well known that the latter modification significantly alters the limiting laws compared to usual M-estimation. We establish the consistency and the asymptotic normality of our sparse penalized M-estimator and we prove the asymptotic oracle property with pseudo-observations, possibly in the case when the number of parameters is diverging. Our framework allows to manage copula-based loss functions that are potentially unbounded. Additionally, we state the weak limit of multivariate rank statistics for an arbitrary dimension and the weak convergence of empirical copula processes indexed by maps. We apply our inference method to Canonical Maximum Likelihood losses with Gaussian copulas, mixtures of copulas or conditional copulas. The theoretical results are illustrated by two numerical experiments.
Journal of Multivariate Analysis, 2022
Meta-elliptical copulas are often proposed to model dependence between the components of a random... more Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map g, called a density generator. When the latter correlation matrix can easily be estimated from pseudo-samples of observations, this is not the case for the density generator when it does not belong to a parametric family. We state sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of g are then proposed, by Mestimation, simulation-based inference or by an iterative procedure available in a R package. Some simulations illustrate the relevance of the latter method.
Journal of the American Statistical Association, 2022
This paper deals with robust inference for parametric copula models. Estimation using Canonical M... more This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean Discrepancy (MMD) principle. We derive non-asymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on [0, 1] d , as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available.
We provide conditions for the existence and the uniqueness of strictly stationary solutions of th... more We provide conditions for the existence and the uniqueness of strictly stationary solutions of the Vine-GARCH process. The proof is based on Tweedie's (1988) criteria, after rewriting the Vine-GARCH process as a nonlinear Markov chain. Furthermore, we provide asymptotic results of the estimators obtained by the quasimaximum likelihood method. We prove the weak consistency and asymptotic normality of the quasi-maximum likelihood estimator obtained in a two-step procedure.
cutting BLOCKINedge. BLOCKINcRedit BLOCKINdeRiVAtiVeS paper of Li (2000), the Gaussian copula mod... more cutting BLOCKINedge. BLOCKINcRedit BLOCKINdeRiVAtiVeS paper of Li (2000), the Gaussian copula model has become the market standard of the structured credit derivatives world. By postulating a correlation structure for the default times of each issuer directly, this model allows the practitioner to price collateralised debt obligation (CDO) payouts and gives a simple solution for their risk management. However, the choice of the pairwise correlations appears largely arbitrary and lacks a clear link with a concept of realised correlation that could be estimated from credit default swap (CDS) prices. After the dramatic collapse in the value of numerous CDOs during the credit crunch, some people have even called Li's formula 'the formula that killed Wall Street'. A common argument against the Gaussian copula model is its lack of replication arguments , contrary to the Black-Scholes model. Option pricing theory relies heavily on the concepts of implied and realised volatiliti...
SSRN Electronic Journal, 2021
Les professions et leurs sociologies
On a coutume de dire qu’une bonne nomenclature doit être révisée tous les vingt ans. Implicitemen... more On a coutume de dire qu’une bonne nomenclature doit être révisée tous les vingt ans. Implicitement, ce principe inspira l’INSEE lorsque l’Institut se lança en 1996 dans une opération de rénovation de la nomenclature des professions et catégories socioprofessionnelles qui datait de 1982. Pour saisir la logique et l’ampleur de cette opération, un bref rappel historique s’impose. Deux audits sur la PCS avaient été demandés à l’Inspection générale de l’Insee en 1996. Le premier, confié à Jean-Mar..
Journal of Risk, 2018
Les documents de travail ne reflètent pas la position du CREST et n'engagent que leurs auteurs. W... more Les documents de travail ne reflètent pas la position du CREST et n'engagent que leurs auteurs. Working papers do not reflect the position of CREST but only the views of the authors.
Annals of Economics and Statistics, 2018
When markets are stressed, volatilities and correlations tend to increase jointly, and volatiliti... more When markets are stressed, volatilities and correlations tend to increase jointly, and volatilities often react quicker than correlations. Based on this intuition, we extend the Dynamic Conditional Correlation model (Engle, 2002) in order to check whether the individual volatilities and/or the probabilities that some assets belong to a high/low volatility regime influence their correlation dynamics. We evaluate potential asymmetrical leverage effects too. We apply our methodology to MSCI Developed Markets indexes that cover twenty-three countries. The new models provide better in-sample fits and forecasts of the portfolio return distributions. Therefore, they are valuable frameworks for portfolio allocation and financial risk management.
Dependence Modeling, 2019
We study nonparametric estimators of conditional Kendall’s tau, a measure of concordance between ... more We study nonparametric estimators of conditional Kendall’s tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide “direct proofs” of the consistency and the asymptotic law of conditional Kendall’s tau. A simulation study evaluates the numerical performance of such nonparametric estimators. An application to the dependence between energy consumption and temperature conditionally to calendar days is finally provided.
Computational Statistics & Data Analysis, 2019
We show how the problem of estimating conditional Kendall's tau can be rewritten as a classificat... more We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (value of −1) conditionally on some covariates. We prove the consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators, including the equivalent of the logit and probit regressions in our framework. Then, we detail specific algorithms adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, we apply all these estimators to a dataset of European stock indices.
Journal of Time Series Analysis, 2018
We derive tests of stationarity for continuous univariate time series by combining changepoint te... more We derive tests of stationarity for continuous univariate time series by combining changepoint tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. Rank-based cumulative sum tests based on the empirical distribution function and on the empirical autocopula at a given lag are considered first. The combination of their dependent p-values relies on a joint dependent multiplier bootstrap of the two underlying statistics. Conditions under which the proposed combined testing procedure is asymptotically valid under stationarity are provided. After discussing the choice of the maximum lag to investigate, extensions based on tests solely focusing on secondorder characteristics are proposed. The finite-sample behaviors of all the derived statistical procedures are investigated in large-scale Monte Carlo experiments and illustrations on two real data sets are provided. Extensions to multivariate time series are briefly discussed as well.
Dependence Modeling, 2017
We discuss the so-called “simplifying assumption” of conditional copulas in a general framework. ... more We discuss the so-called “simplifying assumption” of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.
Advances in Risk Management, 2007
In finance, especially for credit portfolio modeling, basket credit derivatives (CDOs, n-th to de... more In finance, especially for credit portfolio modeling, basket credit derivatives (CDOs, n-th to default) pricing and hedging, the building of an accurate measure of the dependence between the underlying default events is becoming a key-challenge (see Crouhy, Galai and Mark, 2002; Koyluoglu and Hickman, 1998, for a review of the current credit risk portfolio models). This new frontier has induced a huge amount of literature for several years:
SSRN Electronic Journal, 2008
We define a model for managing prepayment, default and interest rate risks simultaneously in stan... more We define a model for managing prepayment, default and interest rate risks simultaneously in standard ABS-type structures (ABS, MBS, CDO of ABS, cash or synthetic). We propose a parsimonious top-down approach: two random factors drive the main underlying risks (prepayment and default), through their current expectations at every time horizon and some volatility assumptions. We get closed-form formulas for pricing all tranches under the assumption that amortization occurs in the most senior tranche only. When the latter assumption is removed, semi-analytical formulas are obtained. The model behavior is illustrated through the empirical analysis of a real synthetic ABS trade.
SSRN Electronic Journal, 2012
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on t... more We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free test statistics and the calculation of reliable p-values are discussed. Some particular cases, like convenient tests for time-dependent copulas, for Archimedean or extreme-value copulas, etc, are dealt with. Finally, the practical performances of the proposed approaches are briefly summarized.
Economie et statistique, 1999
Les horaires de travail dans le couple. Les horaires de travail dépendent fortement des caractéri... more Les horaires de travail dans le couple. Les horaires de travail dépendent fortement des caractéristiques individuelles, notamment du sexe et de la catégorie socioprofessionnelle, mais également des: caractéristiques familiales et de celles du conjoint. Ainsi, pour des couples de salariés à temps complet et à catégorie socioprofessionnelle identique, les femmes travaillent moins longtemps que leur conjoint et leur rythme de travail est plus régulier. Les horaires de départ ou de retour quotidiens de chacun dépendent de leurs positions sociales relatives. La présence de jeunes enfants s'accompagne d'une : réduction de la durée hebdomadaire de travail de la mère, essentiellement par le recours au temps partiel, compensée bien souvent par un allongement de celle du père. Avoir de jeunes enfants amène les parents à des arrangements en termes d'horaires, notamment pour assurer une présence plus longue au domicile. Une approche économétrique originale permet de dépasser ces simples constats : elle se distingue par une modélisation des comportements individuels de chaque conjoint rigoureusement symétrique entre l'homme et la femme et par l'adjonction de la catégorie socioprofessionnelle en tant que variable explicative de la durée du travail. Chez les salariés, un effet d'entraînement joue entre les durées de travail des deux conjoints : plus l'un travaille longtemps, plus l'autre fait de même et inversement. Cet effet est sensiblement plus fort pour la femme que pour l'homme, la présence de jeunes enfants, l'éliminant, sans toutefois aller jusqu'à une compensation des horaires de l'un par ceux de l'autre. La prise en compte des femmes inactives, en. corrigeant le biais de sélection inhérent au phénomène étudié, accuse l'effet de la présence de jeunes enfants. Zusammenfassung Die Arbeitszeiten der Ehepaare. Die Arbeitszeiten hângen in hohem MaBe von den individuellen Merkmalen, insbesondere von derm Geschlecht und der sozio-professionellen Kategorie, aber auch von den familiâren Merkmalen und den Merkmalen. des Ehepartners ab. Bei Ehepaaren, die einer. Vollzeitbeschaftigung, nachgehen und ein und derselben sozio-professionellen Kategorie angehôren, arbeiten die Frauen nicht so lange ; wie ihre Ehepartner und ist ihr Arbeitsrhythmus: regelmâBiger. Die Uhrzeiten, zu denen jeder tàglich zur Arbeit geht und nach Hause kommt, hângen jeweils von der sozialen Stellung ab. Bei Vorhandensein von Kleinkindern nimmt die wôchentliche Arbeitszeit der Mutter ab, im wesentlichen ; durch den Ruckgriff auf eine Teilzeitarbeit, was oftmals durch eine lângere Arbeitszeit des Vaters ausgeglichen wird. Kleinkinderveranlassen die Eltern dazu, Vereinbarungen hinsichtlich der Arbeitszeit zu treffen, insbesondere um zu Hause langer anwesend zu sein. Ein origineller ôkonometrischer Ansatz ermôglicht es, ûber dièse einfachen Feststellungen hinauszugehen. Er zeichnet sich durch eine Modellierung der individuellen, Verhaltensweisen eines jeden Ehepartners, die zwischen Mann und Frau vôllig symmetrisch ist, sowie durch die Hinzufiigung der sozioprofessionellen Kategorie als erklârende Variable der Arbeitszeit aus. Bei den' Arbeitnehmern kommt zwischen den Arbeitszeiten beider ; Ehepartner ein Ankurbelungseffekt zum Tragen: je langer der eine arbeitet, desto langer arbeitet auch der andere. Dieser Effekt ist bei den Frauen starker als bei den Mânnern. Bei Vorhandensein von Kleinkindern findet eim solches «Ûberbieten bei der Arbeit» nicht mehr statt, ohne; daB allerdings die Arbeitszeiten des einen durch diejenigen des anderen ausgeglichen werden. Die-Berucksichtigung der erwerbslosen Frauen unter Berichtigung der dem untersuchten Phanomen inhârenten Selektionsverzerrung, bestàtigt den Effekt des Vorhandenseins von Kleinkindern. Resumen Los horarios de trabajo en la pareja. Los horarios de trabajo dependen mucho de las caracteristicas individuals, ante todo del tipo y de la categorîa socioprofesional, y también de las caracten'scticas familiares y de las del cônyuge. Asf, para parejas de asalariados a tiempo completo y a. categoria socioprofesional idéntica, las mujeres trabajan menos tiempo que su cônyuge y su ritmo de trabajo es mâs regular. Los horarios de idas y de vueltas cotidianas de cada uno dependen de sus posiciones sociales: relativas. La presencia de hijos jôvenes va junta con una reducciôn de la duraciôn semanal del trabajo de la madré, debida-ante todo al recurso al tiempo parcial, compensada muy a menudo por un aumento de la del padre. Tener hijos jôvenes implica que los padres modifiquen sus horarios,-ante todo para garantizar una mayor presencia en casa.. Un enfoque econométrico original permite ir mâs alla de estos meros hechos : se serïala por una modelizaciôn de los comportamientos individuales de cada cônyuge rigurosamente simétrica entre el hombre y la mujer y por, la adjunciôn de la categoria socioprofesional como variable explicativa de la duraciôn laboral: Entre los. asalariados existe una emulaciôn en cuanto a duraciôn. laboral de los dos cônyuges : cuanto mâs tiempo trabaja. uno, mâs trabaja el otro. Este fenômeno es mâs fuerte para la mujer que para el hombre. La presencia de hijos jôvenes élimina esta « emulaciôn laboral », sin llegar sin ; embargo a que los horarios de uno compensen los del otro. La toma en cuenta de las mujeres inactivas, tras corregir el sesgo de selecciôn inhérente al fenômeno; estudiado, acentûa el efecto de la presencia de hijos jôvenes.
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Papers by Jean-David Fermanian