GOURIEROUX Christian

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We introduce new semi-parametric models for the analysis of rates and proportions, such as proportions of default, (expected) loss-given-default and credit conversion factor encountered in credit risk analysis. These models are especially convenient for the stress test exercises demanded in the current prudential regulation. We show that the Least Impulse Response Estimator, which minimizes the estimated effect of a stress, leads to consistent parameter estimates. The new models with their associated estimation method are compared with the other approaches currently proposed in the literature such as the beta and logistic regressions. The approach is illustrated by both simulation experiments and the case study of a retail P2P lending portfolio.

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We introduce new semi-parametric models for the analysis of rates and proportions, such as proportions of default, (expected) loss-given-default and credit conversion factor encountered in credit risk analysis. These models are especially convenient for the stress test exercises demanded in the current prudential regulation. We show that the Least Impulse Response Estimator, which minimizes the estimated effect of a stress, leads to consistent parameter estimates. The new models with their associated estimation method are compared with the other approaches currently proposed in the literature such as the beta and logistic regressions. The approach is illustrated by both simulation experiments and the case study of a retail P2P lending portfolio.

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We introduce Negative Binomial Autoregressive (NBAR) processes for (univariate and bivariate) count time series. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial conditional and marginal distributions. The process is then extended to the bivariate case with a Wishart autoregressive matrix intensity process. The NBAR processes are Compound Autoregressive, which allows for simple stationarity condition and quasi-closed form nonlinear forecasting formulas at any horizon, as well as a computationally tractable generalized method of moment estimator. The model is applied to a pairwise analysis of weekly occurrence counts of a contagious disease between the greater Paris region and other French regions.

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We introduce new semi-parametric models for the analysis of rates and proportions, such as proportions of default, (expected) loss-given-default and credit conversion factor encountered in credit risk analysis. These models are especially convenient for the stress test exercises demanded in the current prudential regulation. We show that the Least Impulse Response Estimator, which minimizes the estimated effect of a stress, leads to consistent parameter estimates. The new models with their associated estimation method are compared with the other approaches currently proposed in the literature such as the beta and logistic regressions. The approach is illustrated by both simulation experiments and the case study of a retail P2P lending portfolio.

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We introduce new models for analyzing the mortality dependence between individuals in a couple. The mortality risk dependence is usually taken into account in the actuarial literature by introducing special copulas with continuous density. This practice implies symmetric effects on the remaining lifetime of the surviving spouse. The new model allows for both asymmetric reactions by means of a Freund model, and risk dependence by means of an unobservable common risk factor (or frailty). These models allow for distinguishing in the lifetime dependence the component due to common lifetime (frailty) from the jump in mortality intensity upon death of spouse (Freund model). The model is applied to the pricing of insurance products such as joint life policy, last survivor insurance, or contracts with reversionary annuities. A discussion of identification is also provided.

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This thesis presents several extensions to positive affine interest rate models. A first chapter introduces the concepts related to the models used in the following chapters. It details the definition of so-called affine processes, and the construction of asset price models obtained by non-arbitrage. Chapter 2 proposes a new estimation and filtering method for linear-quadratic state-space models. The next chapter applies this estimation method to the modeling of interbank spreads in the Eurozone, in order to decompose the fluctuations related to default and liquidity risk. Chapter 4 develops a new technique to create multivariate affine processes from their univariate counterparts, without imposing conditional independence between their components. The last chapter applies this method and derives a multivariate affine process in which some components can remain at zero for extended periods. Incorporated into an interest rate model, this process can efficiently account for zero-bottom rates.

This thesis contributes in four chapters to the analysis and measurement of systemic risk. The first chapter discusses the notion of systemic risk and details the methodological issues of its modeling. The second chapter proposes a structural model of solvency contagion. This equilibrium model allows us to measure the risk of contagion by distinguishing the direct effect of a shock from its propagation. In the third chapter, we provide a framework for valuing an institution's debt that takes into account the effect of interconnections between institutions. We calculate a risk premium specifically related to interconnections. In the fourth chapter, we model the joint effects of shocks to the assets and liabilities of a financial institution. We adapt standard risk measures to identify market, funding, and market liquidity risks. Finally, we explain how to determine the composition and level of regulatory reserves to limit default risk.

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A characteristic of hedge funds is not only an active portfolio management, but also the allocation of portfolio performance between different accounts, which are the accounts for the external investors and an account for the management firm, respectively. Despite lack of transparency in hedge fund market, the strategy of performance allocation is publicly available. This paper shows that, for the High-Water Mark Scheme, these complex performance allocation strategies might explain empirical facts observed in hedge fund returns, such as return persistence, skewed return distribution, bias ratio, or implied increasing risk appetite.

Much research into financial contagion and systematic risks has been motivated by the finding that cross-market correlations (resp. coexceedances) between asset returns increase significantly during crisis periods. Is this increase due to an exogenous shock common to all markets (interdependence) or due to certain types of transmission of shocks between markets (contagion)?Darolles and Gourieroux explain that an attempt to convey contagion and causality in a static framework can be flawed due to identification problems. they provide a more precise definition of the notion of shock to strengthen the solution within a dynamic framework.This book covers the standard practice for defining shocks in SVAR models, impulse response functions, identitification issues, static and dynamic models, leading to the challenges of measurement of systematic risk and contagion, with interpretations of hedge fund survival and market liquidity risks.

"The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gourieroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate even when the portfolio size is large".

This thesis aims at developing tools and models adapted to the study of certain spatial and networked risks. It is divided into five chapters. The first one consists in a general introduction, containing the state of the art within which the various works are included, as well as the main results obtained. Chapter 2 proposes a new multi-site precipitation generator. It is important to have models capable of producing statistically realistic precipitation series. While the models previously introduced in the literature are mainly concerned with daily precipitation, we develop an hourly model. It involves only one equation and thus introduces a dependence between occurrence and intensity, processes often considered as independent in the literature. It includes a common factor taking into account the large-scale atmospheric conditions and a multivariate autoregressive spillover term, representing the local rainfall propagation. In spite of its relative simplicity, this model reproduces very well the intensities, the durations of drought as well as the spatial dependence in the case of Northern Brittany. In Chapter 3, we propose a method for estimating max-stable processes, based on simulated likelihood techniques. Max-stable processes are very well suited to the statistical modelling of spatial extremes, but their estimation is delicate. Indeed, the multivariate density does not have an explicit form and standard estimation methods related to the likelihood cannot be applied. Under appropriate assumptions, our estimator is efficient when the number of temporal observations and the number of simulations tend to infinity. This simulation approach can be used for many classes of max-stable processes and can provide better results than current methods using composite likelihood, especially in the case where only a few time observations are available and the spatial dependence is important.

A characteristic of hedge funds is not only an active portfolio management, but also the allocation of portfolio performance between different accounts, which are the accounts for the external investors and an account for the management firm, respectively. Despite a lack of transparency in hedge fund market, the strategy of performance allocation is publicly available. This paper shows that, for the High WaterMark Scheme, these complex performance allocation strategiesmight explain empirical facts observed in hedge fund returns, such as return persistence, skewed return distribution, bias ratio, or implied increasing risk appetite.

The ratings of fund managers based on past performances of the funds and the rating dynamics are crucial information for investors. This paper proposes a stochastic migration model to investigate the dynamics of performance-based ratings of funds, for a given risk-adjusted measure of performance. We distinguish the absolute and relative ratings and explain how to identify their idiosyncratic and systematically persistent (resp. amplifying cycles) components. The methodology is illustrated by the analysis of hedge fund returns extracted from the TASS database for the period 1994–2008.

This paper analyses how an external adverse shock will impact the financial situations of banks and insurance companies and how it will diffuse among these companies. In particular we explain how to disentangle the direct and indirect (contagion) effects of such a shock, how to exhibit the contagion network and how to detect the ”superspreaders”, i.e. the most important firms involved in the contagion process. This method is applied to a network of 8 large European banks in order to analyze whether the revealed interconnections within these banks differ depending on the underlying measure of banks’ financial positions, namely their market capitalization, the price of the CDS contract written on their default and their book value.

This paper analyses how an external adverse shock will impact the financial situations of banks and insurance companies and how it will diffuse among these companies. In particular we explain how to disentangle the direct and indirect (contagion) effects of such a shock, how to exhibit the contagion network and how to detect the ”superspreaders”, i.e. the most important firms involved in the contagion process. This method is applied to a network of 8 large European banks in order to analyze whether the revealed interconnections within these banks differ depending on the underlying measure of banks’ financial positions, namely their market capitalization, the price of the CDS contract written on their default and their book value.

In addition to active portfolio management, hedge funds are characterized by the allocation of portfolio performance between the external investors and the management firm accounts. This allocation can take different forms, such as the Loss Carry Forward scheme, and some of them can be coupled with performance smoothing techniques. This paper shows that this additional smoothing component might explain some empirical facts observed on the distribution and the dynamics of hedge fund returns.

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The first part of this thesis introduces a new methodology for conducting stress-testing exercises. Our approach allows to consider much richer stress scenarios than in practice, which evaluate the impact of a change in the statistical distribution of factors influencing asset prices, not only the consequences of a particular realization of these factors, and take into account the reaction of the portfolio manager to the shock. The second part of the thesis is devoted to the valuation of bonds with very long maturities (over 10 years). Modeling the volatility of very long term rates is a challenge, especially because of the constraints posed by the absence of arbitrage opportunities, and most models of interest rates in the absence of arbitrage opportunities imply a constant (infinite maturity) rate limit. The second chapter studies the compatibility of the "level" factor, whose variations have a uniform impact on all the rates modeled, especially the longest ones, with the absence of arbitrage opportunities. In the third chapter, we introduce a new class of interest rate model, without arbitrage opportunities, where the limit rate is stochastic, and we present its empirical properties on a database of US Treasury bond prices.

The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe disability. Because of the significant costs of long term care facilities, it is important to analyze the time spent in long term care, as well as the probability of entering into this state during its lifetime, and how they evolve with longevity. Our paper considers such questions, when lifetime data are available, but long term care data are either unavailable, or too aggregated, or unreliable, as it is usually the case. We specify a joint structural model of long term care and mortality, and explain why parameters of such models are identifiable from only the lifetime data. The methodology is applied to the mortality data of French males, first with a deterministic trend and then with a dynamic factor process. Prediction formulas are then provided and illustrated using the same data. We show in particular that the expected cost of the long term care is increasing less fast than the residual life expectancy at age 50.

Financial institutions are confronted with various risks in the performance of their functions, including credit risk, market risk and operational risk. The instability of these factors weakens these institutions and makes them vulnerable to financial risks which, for their survival, they must be able to identify, analyze, quantify and manage appropriately. Among these risks, the one linked to credit is the most feared by banks, given its capacity to generate a systemic crisis. The probability of an individual moving from a non-risky state to a risky state is thus at the heart of many economic questions. In credit institutions, this issue is expressed in terms of the probability that a borrower will move from a "good risk" state to a "bad risk" state. For this quantification, credit institutions are increasingly using credit scoring models. This thesis focuses on current credit-scoring techniques adapted to the needs of a credit institution, the CFCAL-bank, specialized in mortgage-backed loans. In particular, we present two non-parametric models (SVM and GAM) whose performance in terms of classification is compared with that of the logit model traditionally used in banks. Our results show that SVMs perform better if we are only interested in the global predictive capacity. However, they exhibit lower sensitivities than the logit and GAM models. In other words, they predict defaulting borrowers less well. In the current state of our research, we advocate GAM models, which admittedly have lower overall predictive ability than SVMs, but give more balanced sensitivities, specificities, and predictive performance. By highlighting targeted credit scoring models, applying them to real mortgage data, and comparing them through their classification performance, this thesis makes an empirical contribution to the research on credit scoring models.

This article proposes an overview of the usefulness of the regime switching approach for building various kinds of bond pricing models and of the roles played by the regimes in these models. Both default-free and defaultable bonds are considered. The regimes can be used to capture stochastic drifts and/or volatilities, to represent discrete target rates, to incorporate business cycles or crises, to introduce contagion, to reproduce zero lower bound spells, or to evaluate the impact of standard or nonstandard monetary policies. From a technical point of view, we stress the key role of Markov chains, Compound Autoregressive (Car) processes, Regime Switching Car processes and multihorizon Laplace transforms.

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In this paper we examine the dependence between the liquidation risks of individual hedge funds. This dependence can result either from common exogenous shocks (shared frailty), or from contagion phenomena, which occur when an endogenous behaviour of a fund manager impacts the Net Asset Values of other funds. We introduce dynamic models able to distinguish between frailty and contagion phenomena, and test for the presence of such dependence effects, according to the age and management style of the fund. We demonstrate the empirical relevance of our approach by measuring the magnitudes of contagion and exogenous frailty in liquidation risk dependence in the TASS database. The empirical analysis is completed by stress-tests on portfolios of hedge funds.

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This research concerns the use of auxiliary information in survey theory. The fact that there is no UMVUE (unbiased estimator with uniformly minimum variance) for the total and the lack of information about the likelihood function force survey statisticians to use specific techniques to construct more efficient estimators, among which are the ratio estimator, the regression estimator and the margin calibration estimator. Sometimes, we have complete auxiliary information, in the form of distribution functions of real variables. This information is much more detailed than the knowledge of the totals alone. The margin calibration method therefore requires an adaptation to use the knowledge of distribution functions, which is equivalent to a much larger, possibly infinite, number of totals. The main objective of this research is to generalize the margin calibration technique by developing methods for using this information, called distribution function calibration methods. Three approaches have been proposed: parametric, semi-parametric and non-parametric calibration. Generalizations to rank calibration and moment calibration are also proposed. An in-depth study on two-stage, two-phase and two-dimensional systematic sampling is also provided as systematic sampling is a special case. A study on the estimation of the distribution function and the fractiles of a finite population is presented in the last chapter because the estimation of the distribution function is a component of some methods developed for the calibration on the distribution function. On the other hand, the estimation of the distribution function and fractiles of a finite population is in itself an interesting topic in survey theory, to which survey statisticians have recently given much attention. Numerical examples on simulated and real data are presented to test the different methods developed in this research. The simulations show that the distribution function estimators are in general more accurate than the marginally calibrated estimator.

This work consists of five chapters and examines two aspects of term structure modeling: the valuation of interest rate derivative assets and the inference of models typically used in this valuation. The first chapter consists of an introduction to continuous-time models and their arbitrage valuation. The second chapter focuses on the valuation of options in a particular affine model. The estimation of diffusion processes describing the dynamics of state variables is analyzed in chapter iii and consists in a presentation of a method based on simulations. In chapter iv, non-nested hypothesis tests using simulation-based procedures and a notion of indirect embedding are described. Two applications are proposed in chapter v. The first is the presentation of a method for estimating bond prices from term structure models. The second application concerns the estimation and comparison of several models usually used for the instantaneous short rate.

The first part of this paper presents asset pricing models based on the principle of no arbitrage opportunities and compatible with statistical analysis. Such models are described in discrete time. We first focus on the study of the term structure of interest rates and on the estimation of such a model from the observation of fixed income bonds. We then extend the proposed approach to more complex securities. We then describe a valuation model where statistical randomness appears in the price dynamics of elementary contingent assets. The properties of this model are studied when the price law of the elementary contingent assets is a gamma measure and we show in particular that it allows to generalize classical valuation formulas. The second part of this thesis is devoted to estimation problems in diffusion processes. First, we present the different parametric or nonparametric estimation methods by classifying them by asymptotics. Then we study the properties of parametric estimators of a diffusion from discrete time observations, with a fixed step. The estimation methods used are methods based on simulations of the process: simulated moments and indirect inference. We focus on establishing explicit links between the different asymptotics that appear and the number of observations.

We study the convergence in probability of the maximum likelihood estimator of an ARMA model whose errors follow a GARCH (1, 1) process according to the specification of Baba, Engle, Kraft and Kroner. We establish conditions for the existence of moments of order greater than two. The conditions of strict stationarity and ergodicity of some constrained models are presented. Finally, we propose a general framework for the continuous time approximation of multivariate ARCH models.

This thesis is devoted to the study of granger causality tests. One of the important characteristics of these tests is the assumption of stationarity of the series. This work considers non-stationary (integrated series of order one), admitting a finite vector autoregressive (var) representation whose coefficients are constant in time. In this case, the absence or presence of cointegration influences the causality tests. In the presence of cointegration, toda and philips propose a new method, consisting in constructing statistics in an error correction model (ecm), however, the formulas of their statistics are complicated. We then propose simpler formulas. They are built from the ecrm model. They converge to a chi-square distribution. Moreover, this thesis extends the research to series with deterministic tendency of degree one. This leads to propose three definitions of cointegration: stochastic cointegration, deterministic cointegration and global cointegration. Our work considers three ecm forms, derived from a finite var model, according to the level of consideration of the constraints on the coefficient of the time term. This work performs: (1) the comparison of these three ecm forms on the theoretical economic level, (2) the study of the consequences of the bad estimation of the johansen ecm model (based on the specific deterministic trend), (3) the proposal of the statistics of the global cointegration test, (4) the modifications of the formulas of the proposed statistics concerning the causality tets. Various simulations are also carried out, in order to compare the considered statistics.

The theory of portfolio choice is generalized to allow for a greater heterogeneity of risk asset choices. The theory is represented in a static and dynamic framework. Statistical inference methods are proposed. They concern either detailed market data (prices and portfolio yields) or qualitative information on agents' holdings of financial assets.

This thesis presents econometric analyses of transitions between different labor market states such as employment, unemployment and inactivity. We emphasize the importance of introducing non-stationarity in the modeling of labor market transitions. We obtain estimates on samples extracted from the INSEE employment surveys.

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This work is based on the introduction of thresholds in time series models. We start by presenting the theory of homogeneous Markov chains, necessary for the study of nonlinear processes. Autoregressive models of order one with a threshold are the subject of the second part. Distributional properties are obtained in the neighborhood of the linear model, which allows to obtain approximate formulas for various quantities: mean, variance, moments... . Finally, two methods for testing the linearity hypothesis are proposed. The next part proposes a new class of ARCH (autogressive conditionally heteroskedastic) models. The introduction of thresholds in the specification of the conditional variance allows to take into account specific effects on the volatility (persistence, asymmetry according to the sign of the prior errors...). A complete study is proposed: weak stationarity, strict stationarity, computation of moments, analysis of the leptokurtic effect, comparison with ARCH models, estimation of various parameters, test of the homoscedasticity hypothesis. Finally, the last part of the thesis deals with the transition to continuous time of heteroscedastic threshold models.