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Revisiting Identification in Structural VAR Models

C. Gouriéroux, A. Monfort

Abstract : Structural VAR (SVAR) or VARMA models are usually derived from the equilibrium business cycle models, or as the exact or log-linear approximation of Dynamic Stochastic General Equilibrium (DSGE) models. The underlying structural models imply various restrictions, such as constraints on the autoregressive coefficients, economic interpretation of some shocks in terms of preference, technology, taxation, or information, or the non invertibility of the moving average or autoregressive dynamics, called nonfundamentalness in the literature. The SVAR models are usually estimated by the standard Box-Jenkins (BJ) approach, coming up against two identification issues : i) the BJ approach estimates the fundamental representation of the process, which is not necessarily the representation with economic interpretation; ii) the economic shocks are known up to some rotation. These identification problems have important implications on the impulse response functions that represent the effects of economic shocks. The aim of this note is to explain that these difficulties are mainly due to the Gaussian assumption underlying the BJ approach, and that the identification issues are solved in a non Gaussian framework. Thus "there is no non-uniqueness problem endemic to moving-average representation".  


Banks, Sovereign Risk and Unconventional Monetary Policies

S. Auray, A. Eyquem, X. Ma

Abstract : We develop a two-country model with an explicitly microfounded interbank market and sovereign default risk. Calibrated to the Euro Area, the model performs satisfactorily in matching key business cycle facts on real, financial and fiscal time series. We then use the model to assess the effects of a large crisis and quantify the potential effects of alternative unconventional policies on the dynamics of GDP, sovereign default risk and public indebtedness. We show that quantitative monetary easing is more efficient in stimulating GDP, while qualitative monetary easing relieves financial tensions and sovereign risk more efficiently. In terms of welfare, in the short run, unconventional monetary policies bring sizable welfare gains for households, while the long term effects are much smaller. 


Procyclicité des régulations des marchés financiers

S. Auray,  C. Gouriéroux

Extraits : La récente crise financière et économique a montré que [le] nouvel environnement était encore mal compris et que certaines politiques ou régulations avaient pu être à la source de la crise et l'avoir amplifiée. Dans la "chasse au coupable" et dans les débats, souvent biaisés et peu argumentés qui ont suivi, ont été évoqués le rôle de la finance mathématique, celui des agences de notation, la politique économique des États-Unis, l'absence de régulation (les trous noirs de la finance, i.e. le shadow banking), la rapacité des banquiers, la procyclicité de certaines régulations financières... […] Nous nous proposons dans cette note de revenir de façon, nous l'espérons, plus sereine et plus argumentée sur cet aspect de procyclicité des régulations1 financières, incluant notamment celles du crédit, des banques et compagnies d'assurance, et celles des marchés financiers. […] Les régulations financières peuvent également avoir un impact sur les éventuels cycles de l'économie réelle. Cet aspect est évoqué dans la partie 3 qui se veut être une partie d'éléments de conclusion, où nous insistons sur la nécessité de régulations micro-prudentielles et non seulement macro-prudentielles pour effectuer une gestion fine de ces phénomènes. Enfin, nous ouvrons le débat sur la question de qui devrait être le décideur final de la politique économique. Cette note ne prétend en  rien à l'exhaustivité au regard de l'étendue de la littérature sur le sujet, mais a pour objet d'ouvrir le débat sur la régulation des marchés ou des cycles dont on questionne l'existence. Elle cherche à éclairer le lecteur sur ce qui devrait ou pourrait être régulé.


The Limits of Granularity Adjustments

J.D. Fermanian

Abstract : We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogeneous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail all the technical conditions of validity and provide an upper bound of the remainder term at a finite distance. Moreover, we deal explicitly with the case of general loss distributions, possibly with masses. For some simple portfolio models, we prove empirically that the granularity adjustments do not always improve the infinitely granular first-order approximations. This stresses the importance of checking some conditions of regularity before relying on such techniques. Smoothing the underlying loss distributions through random recoveries or exposures improves the GA performances in general.


Natural Disasters: Exposure and Underinsurance

C. Grislain-Letrémy

Abstract : Insurance coverage for natural disasters remains low in many exposed areas. A limited supply of insurance is commonly identified as a primary causal factor in this low insurance coverage. The French overseas departments provide a rare natural experiment of a well-developed supply of natural disasters insurance in highly exposed regions. The French system of natural disasters insurance is underwritten and regulated by the French government; instituted initially for metropolitan France only, it was extended to overseas departments in the state of emergency following Hurricane Hugo in 1989. This natural experiment makes it possible to analyze the determinants of insurance coverage on the demand side. Based on unique household-level microdata, I estimate an insurance market model which had not yet been empirically tested. Using this structural approach, I show that underinsurance in the French overseas departments is neither due to perception biases nor to unaffordable insurance, but mainly to uninsurable housing and to the anticipation of assistance, which crowds out insurance. Individual insurance decisions are influenced by neighbors’ insurance choices through peer effects and neighborhood eligibility for assistance.


Allocating Systemic Risk in a Regulatory Perspective

C. Gouriéroux, A. Monfort

Forthcoming in International Journal of Applied and Theoretical Finance

Abstract : The paper proposes an axiomatic approach for allocating aggregate risk among individual entities. It is shown that a risk allocations system should obey two axioms. The allocations satisfying these axioms are called coherent risk contributions and are characterized. In the paper the contribution of each entity is decomposed into a systemic part, an unsystemic part and, possibly, a cross effect.  Consequences in terms of regulation are discussed.

Pricing Default Events : Surprise, Exogeneity and Contagion

C. Gouriéroux, A. Monfort, J.P. Renne

Forthcoming in Journal of Econometrics

Abstract : In oder to derive closed-form expressions of the prices of credit derivatives, standard credit-risk models typically price the default intensities, but not the default events themselves. The default indicator is replaced by an appropriate prediction and the prediction error, that is the default-event surprise, is neglected. Our paper develops and approach to get closed-form expressions for the prices of credit derivatives written on multiple names without neglecting default-event surprises. This approach differs from the standard one, since the default counts necessarily cause the factor process under the risk-neutral probability, even if this is not the case under the historical probability. This implies that the standard exponential pricing formula of default does not apply. Using U.S. bond data, we show that allowing for the pricing of default events has important implications in terms of both datafitting and model-implied physical probabilities of default. In particular, it may provide a solution to the credit spread puzzle. Besides, we show how our approach can be used to account for the propagation of defaults on the prices of credit derivatives.


Liquidation Equilibrium with Seniority and Hidden CDO

C. Gourieroux, J.C. Heam, A. Monfort  

Forthcoming in Journal of Banking and Finance

Abstract: The aim of our paper is to price credit derivatives written on a single name when this name is a bank. Indeed, due to the special structure of the balance sheet of a bank and to the interconnections with other institutions of the financial system, the standard pricing formulas do not apply and their use can imply severe mispricing. The pricing of credit derivatives written on a single bank name requires a joint analysis of the risks of all banks directly or indirectly interconnected with the bank of interest. Each name cannot be priced in isolation, but the banking system must be treated as a whole. It is necessary to analyze the contagion of losses among banks, especially the equilibrium of joint defaults and recovery rates at liquidation time. We show the existence and uniqueness of such an equilibrium. Then the standard pricing formulas are modified by adding a premium to capture the contagion effects.


The Risk Map: A new tool for validating risk models

G. Colletaz, C. Hurlin, C. Pérignon

Journal of Banking & Finance, 2013, 37, 10, 3843-3854

Abstract: This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.


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