Working Group on (quantitative) Risk Analysis / Uncertainty - ESSEC Business School - with the support of the group BFA (Banque Finance Assurance) of the SFdS (Société Française de Statistique) Organizer: Prof. Marie Kratz
The main objective is the resolution of concrete problems which affect the industry or of subjects of public interest, in the field of (quantitative) risk analysis, creating new tools or methods. Many skills are today distributed in various domains, financial, industrial, academic,..., therefore the intention behind the creation of this group is:
To this end, regular meetings will include:
Each participant might propose a precise theme, a work on a given article or on a project. The presentation slides are in general available: see the attachments at the end of the page. Our one hour meetings will take place generally twice a month, on Wednesdays or Thursdays.
If you are interested and want to be part of the mailing list, please contact Marie Kratz. Calendar of the meetings in 2011-12: 2nd Term: February 7 (Tuesday), 12:30pm, La Défense EEE (Cnit), room 203: Seminar by Dr. Corina Constantinescu University of Liverpool on "Risk processes with premium adjusted to solvency targets" Abstract: The traditional point of view of ruin theory is reversed: rather than studying the probability of ruin as a function of the initial reserve under a fixed premium, we adjust the premium so as to obtain a given ruin probability (solvency requirement) for a fixed initial reserve (the financial capacity of the insurer). This is joint work with Veronique Maume-Deschamps and Ragnar Norberg. February 29, 1 2:30 pm, La Défense EEE (Cnit), room 236, Seminar by O. Lopez (UPMC Paris 6) March 14, 1 2:30 pm, La Défense EEE (Cnit), room 237, Seminar by W. Dick (ESSEC Business School) March 21, 1 2:30 pm, La Défense EEE (Cnit), room 202, Seminar by J-P. Boutard (Fiducial Audit); to be confirmed March 28, 1 2:30 pm, La Défense EEE (Cnit), room 101, Seminar by B. Maillet ( ABN AMRO & Univ. Orléans); to be confirmed.January 18, 1 2:30 pm, La Défense EEE (Cnit), room 236, Seminar by Thierry Roncalli ( Head of Research&Development, Lyxor Asset Management & Evry Univ.): Portfolio Optimization versus Risk-Budgeting Allocation. Abstract: Portfolio allocation is generally based on optimization method (Minimum variance, Markowitz, Merton, Black-Litterman, etc.). The first part of this presentation is to show that portfolio optimization faces several drawbacks in terms of concentration, stability and management. We will show that risk-budgeting techniques is an alternative method which appears more robust. In particular, we will focus the second part of the presentation in one of the most simple risk-budgeting methods, when the risk budgets are the same. In this case, we obtain the ERC (Equal Risk Contribution) portfolio. After giving the mathematical properties of the ERC portfolio, we will present some applications to manage equity funds (like alternative-weighted indexes) and diversified funds (like risk parity funds). In the third part of the presentation, we will focus on risk-budgeting methods, when the risk budgets are not the same. We will generalize some properties of the ERC portfolio and present an application to manage the sovereign credit risk in bond portfolios. 1st Term: December 14, 12:30 pm, SCOR auditorium (with the support of SCOR Group), La Défense: Seminar by Pierre Miehe (Deputy CE0, ACTUARIS International): Risk Management in Insurance: What technical solutions to answer the huge modeling requirements? Abstract: The new European regulation for insurance “Solvency II” encourages insurers of big/medium size companies to implement internal models for the calculation of their required capital. All risks have to be modeled simultaneously. For the estimation of tails and extreme events 10 000 simulations at least are recommended. For big companies this can theoretically imply runtimes of several weeks… This becomes even worse with the Simulations in Simulations issue. The aim of this presentation is to review a range of solutions to deal with this huge number of simulations, through the analyze of adapted random generators, models optimizations, and potential simplified “artificial intelligence” implementations. November 30 (Wednesday), 12:30 pm, La Défense EEE (Cnit), room 101: Seminar by Jean-Gabriel Attali (Dr, Consultant, Formerly Strategy Analyst at Exane Derivatives): Risk measurement and its limits in asset management. Abstract: Management of risk is a key point in the area of asset management. The aim of this presentation is to address various aspects of risk as well as its measurement or control. In particular, we will focus on the limits of some risk measures, in the sense that risk is often underestimated when it is measured ex-post, especially when the manager is very active or uses derivatives products. We will show that the management of ex-post risk is easy when it is measured by volatility (or Var), even in time of crisis, simply by managing the exposition of the fund. Unfortunately, this technique does not ensure the safety of principal which remains the main objective of the industry of asset management. November 16 (Wednesday), 12:15 pm, La Défense EEE (Cnit), room 104: Seminar by Paul Deheuvels (Prof., UPMC Paris 6): On Difficulties of Risk Modelling and Portfolio Analysis. Abstract: The statistical modelling of insurance claims is typically achieved through lognormal models, which often fit well to the central portion of a number of data sets. What is meant by the “central portion” of observations embraces the set of values, truncated below and above by “appropriate” threshold levels. The most troublesome claim-values are, as could be expected, large observations, but small values may generate other technical difficulties as well, which we will not consider here in detail. Large values typically fall in the domain of reinsurance, and are often quite well interpreted by Pareto-type models. The main difficulty comes here from the available “large” observations, which compose, most of the time, data sets so small as to render their statistical analysis troublesome. We have considered recently a number of portfolios, each composed of a few thousand observations, and observed, in each case, that only a small percentage of the data could be well interpreted by Pareto-type models. Such models become difficult to fit when the number of observations falling in this range is, for example, of the order of 5 to 20. Another class of technical problems to cope with is, first, to find the right statistical assessment methods to compare between each other the respective risks of several portfolios, and second, to assess the goodness-of-fit of a given portfolio with respect to a specified model. In particular, when some large observations fall into the domain of Pareto distributions, the finiteness of claim-values variances is often questionable. Practically all the data sets which we have considered lead to estimations of Pareto indexes for large claims corresponding to finite expectations, but yet, to infinite variances. This, in itself, suffices to support the idea that most “usual” statistical comparison methods (such as that using the Student test technology) are ineffective. We shall illustrate these questions through the analysis of a real data set, and propose some new methods to bring solutions to the corresponding problems. Daniel Zajdenweber (Prof. , Univ. Paris X Nanterre): Extremal Events in a Bank Operational Losses. Abstract: Operational losses are true dangers for banks since their maximal values to signal default are difficult to predict. This risky situation is unlike default risk whose maximum values are limited by the amount of credit granted. For example, our data from a very large US bank show that this bank could suffer, on average, more than four major losses a year. This bank had seven losses exceeding hundreds of millions of dollars over its 52 documented losses of more than $1 million during the 1994-2004 period. The tail of the loss distribution (a Pareto distribution without expectation whose characteristic exponent is 0.95 ! ! ! 1) shows that this bank can fear extreme operational losses ranging from $1 billion to $11 billion, at probabilities situated respectively between 1% and 0.1%. The corresponding annual insurance premiums are evaluated to range between $350 M and close to $1 billion. Keywords: Bank operational loss, value at risk, Pareto distribution, insurance premium, extremal event. Joint work with H. Dahen and G. Dionne (Journal of Operational Risks, 2010). October 20 (Thursday), 12:30 pm, La Défense EEE (Cnit), room 101: Seminar by Jean-Philippe Bruneton (NaXys, Namur Univ., Belgium; formerly Risk Analyst at SCOR Swizerland, Financial modelling team): Diversification benefit in Gaussian Aggregation Trees. Abstract: Insurance risks are often aggregated together with the help of copulas: risks whose individual marginals are known are tied together via some function (the copula). In mathematical language, their joint distribution is defined via the copula. We focus our study on the aggregation of risks within so-called hierarchical trees: A tree of aggregation refers to applying several times such a process, linking some marginals together, then linking the resulting marginals together, and so on and so forth, until the total portfolio is modelised. We study in particular the "Gaussian Tree" where both marginals and copulas are Gaussian. This enables exact anlytical results for the r.v. of the total portfolio, and therefore the exact computation of the diversification benefit (the release in solvency capital due to diversification of risks, but taking into account their interdependencies). Such a toy model enables us to study the impact of the width and depth of the tree on the diversification benefit. We show that "tight trees" diversify better than "fat trees". We also show some numerical results that support this conclusion also outside the Gaussian world: Lognormal Trees aggregated via Gaussian or Clayton copula show the same overall behavior. Calendar of the meetings in 2010-11: 3rd Term: June 16, 12:30 pm, La Défense EEE (Cnit), room 138: Seminar by Blaise Bourgeois (Head of Life Product Risks, AXA, Group Risk Management, Paris): Risk Neutral Valuation in Insurance. Abstract: Insurance markets have traditionnally been presented as incomplete markets, using statistical approaches based on real-world measures to price & evaluate risks, rather than market-consistent valuation methods (aka risk-neutral framework). Whilst this may continue to hold to some extent for Property & Casualty business, the Life & Savings sector has progressively adapted its valuation & risk measurement methodologies and tools to a world more akeen to modern financial markets than traditional actuarial reserving methods. This paper presents the building blocks of these risk-neutral valuation methods / tools now commonly applied by most major L&S insurance companies in Europe. This framework will form from 2013 onwards the backbone of the new Solvency II regulation. Key words: Market-Consistent Embedded Value, Replicating Portfolio, Economic Capital, Dynamic Hedging, Completing Insurance markets June 7, Invitation to the Conference on Mathematical Modeling of Systematic Risk (IHP Paris) see: http://www.proba.jussieu.fr/pageperso/ramacont/SystemicRiskParis2011/ May 19, 12:30 pm, La Défense EEE (Cnit), room 201: Seminar by Nizar Touzi (Prof., Ecole Polytechnique, Palaiseau): Model independent bounds under calibration constraints: a stochastic control approach. Abstract: We develop a stochastic control approach for the derivation of model independent bounds for derivatives under various calibration constraints. Unlike the previous literature, our formulation seeks the optimal no arbitrage bounds given the knowledge of the distribution at some (or various) point in time. By convex duality techniques, this problem is converted into an optimal transportation problem along controlled stochastic dynamics. We also provide precise connections with the Azema-Yor solution of the Skorohod Embedding problem, and we obtain some extensions. May 5, 12:30 pm, La Défense EEE (Cnit), room 101: Seminar by Suzanne Emmer (Dr., UBS, Zürich): Credit Stress Loss. Abstract: After a short overview of currently used credit risk measures and the stress testing landscape we give an introduction to different stress testing methodologies which are applied to the wealth management and business banking portfolio. Abstract: Risk management specialists, practitioners and academics, have paid much attention to estimation of the likelihood of untoward events. Consideration of the fundamental nature of risk as an essentially human construct identifies many other aspects of risk management that deserve at least as much attention as the likelihood of untoward events. April 7, 12:30 pm, La Défense EEE (Cnit), room 236: Seminar by Jean-Paul Renne (Banque de France, Paris), Default, Liquidity and Crises: an econometric framework. Abstract: In this paper, we present a general discrete-time affine framework aimed at jointly modeling yield curves associated with different debtors. The underlying fixed-income securities may differ in terms of credit quality and/or in terms of liquidity. The risk factors follow conditionally Gaussian processes, with drifts and variance-covariance matrices that are subject to regime shifts described by a Markov chain with (historical) non-homogenous transition probabilities. While flexible, the model remains tractable. In particular, bond prices are given by quasi-explicit formulas. Various numerical examples are proposed, including a sector-contagion model and credit-rating modeling. 2nd Term: (there will be only a few meetings since I will be working abroad; we will meet again on a regular basis on the 3rd term). March 24, 12:30 pm, SCOR (La Défense), Auditorium (with the support of the SCOR Group): Seminar by Hansjoerg Albrecher (Prof., HEC Lausanne, Switzerland), On refracted stochastic processes and the analysis of insurance risk. Abstract:
We show a somewhat surprising identity for first passage probabilities of spectrally-negative Levy processes that are Feb. 3, 12pm-1pm, La Défense EEE (Cnit), room 104: Discussion by Laila Elbahtouri (SCOR, Actuary) on the paper by Albrecher et al. "Explicit ruin formulas wit dependence among risks", Insurance: Mathematics and Economics 48 (2011) 265-270 1pm-2pm, La Défense EEE (Cnit), room 104: Seminar by Doug Andrews (Senior lecturer at Univ. of Southampton & Actuary (Fellow of the IA &Canadian IA, SOA)), Risk management considerations for the Canada Pension Plan: a case study. Abstract: What are the risks that the Canada Pension Plan faces and how are they managed? This presentation begins with a review of the governance structure, the actuarial valuation method and the automatic balancing mechanism. It then examines particular assumptions, such as fertility, mortality, migration, productivity and investment. It explains the risks, discusses the methods used to derive the assumptions, and outlines some of the sensitivity tests used to quantify the risk. Jan. 19 (Wednesday, instead of Thursday) 11:15 am, Cergy ESSEC campus, room N305. Seminar by Olivier Wintenberger (Prof., Univ. Paris Dauphine), Limit laws for sums of weakly dependent data with infinite variances. Abstract: Many econometrical models take into account two stylized facts: the dependence structure of the time series (absence of correlations, dependence of the squares) and the high volatility (tails as power laws). If the dependence is not too strong, the asymptotic behavior of the sum is no longer distributed as a normal law but as another type of stable law. Thus, the dependence and the power law marginals drive the limit law in a very intricated way. In a work done with K. Bartkiewicz, A. Jakubowski and T. Mikosch, we suceeded to give a non standard central limit theorem where we clearly determined in the limiting stable law what is due to the dependence and what is due to the marginal law. We apply our result to the sum of the stationary solution of the GARCH(1,1) model. Jan. 12, 12:30pm, La Défense EEE (Cnit), room 202: discussion on projects by groups 1st Term: Dec. 16, 12:30 pm, La Défense EEE (Cnit floor 2 "Bureaux", ESSEC, room 236) Seminar by Véronique Maume-Deschamps (Prof., ISFA Lyon), Some multivariate risk indicators; estimation and application to reserve allocation. Abstract: We consider some risk indicators of vectorial risk processes. These indicators are expected sums of some penalties that each line of business would have to pay due to its temporary potential insolvency. The dependency between lines of business is taken into account. By using stochastic algorithms, we may estimate the minimum of these risks indicators, under a fixed total capital constraint. This minimization may apply to reserve allocation. Dec. 2, 11:15 am, La Défense EEE (Cnit floor 2 "Bureaux", ESSEC, room 237) Seminar by Désiré Binam (Dr., Consultant Front-office), How the trading technology changes the market microstructure. Abstract: The evolution of trading technologies has deeply modified the microstructure of today’s financial markets. We will see how the technology is changing the trading process and strategy and how players deal with new concepts such as Direct Market Access (DMA), Smart Order Routing (SOR), High Frequency Trading (HFT) and Algorithmic trading. Nov. 25, 12:30pm, La Défense EEE (Cnit floor 2 "Bureaux", ESSEC, room 334) Seminar by Philippe Soulier (Prof., Univ. Paris Nanterre), Prediction for time series after catastrophic events. Abstract: We consider the problem of prediction in a time series when the conditioning event is extreme. The quantities of interest are the limiting conditional distribution of future events given that the past was extreme, and the normalizing functions needed to obtain non degenerate these limit laws. I will consider two classes of processes: GARCH-type and stochastic volatility processes. The main difference is the presence or absence of clustering of extremes. Nov. 4, 12:30pm, La Défense EEE (Cnit floor 2, room 237): -Discussion on some projects. -Invitation to the Finance Department Seminar on Nov. 8, 4:30 pm - ESSEC Campus Cergy Pontoise (room N 305) by Heitor Almeida (Univ. Illinois), Aggregate Risk and the Choice between Cash and Lines of Credit. (see https://sites.google.com/a/essec.edu/seminaires-dept-finance/ for the abstract). Oct. 14, 12:30pm, La Défense (Cnit floor 2, room 236): - Set up of the agenda and the topics/objectives for the trimester. - Seminar by Cristina Butucea (Prof., Univ. Marne La Vallée), Various ways to summarize a curve with a number: estimation and applications. Abstract: Curve estimation is very frequently studied in various areas. We shall discuss the pros and cons of parametric versus nonparametric estimation of curves. A good compromise in many examples is to recover less information about the underlying function to be estimated (summarize it) using the nonparametric techniques. We shall discuss several ways to do so and focus on excess mass estimation. Calendar of the meetings in 2009-10: 2nd Term: April 9: 9am-5pm: IHP (Institut Henri Poincaré, 75005 Paris), workshop on "Financial Regulation"; organization: M. Bardos & M.Kratz for the BFA (Banque Finance Assurance) group, SFdS. (download the program; see the attachments). April 1, 6pm La Défense EEE (Cnit floor 1, room 236): seminar by Laurent Ferrara (Banque de France et Univ. Paris Ouest), Assesing the recession risk anticipated by financial markets March 19, Conference IDEI/Scor, "Integration of Extremal Events in Quantitative Risk Management": http://www.idei.fr/conference/conf_scor.html
March 4, 12:30pm, La Défense EEE (Cnit floor 1, room 138): seminar by Marie Kratz (Prof., Essec), On alarm systems. Applications for Insurance companies and for Health surveillance Institute. Feb. 18, 12:30pm, La Défense EEE (Cnit floor 1, room 138): seminar by Marie Kratz (Prof., Essec), On alarm systems. Applications for Insurance companies and for Health surveillance Institute. Feb. 4, 12:30pm, La Défense EEE (Cnit floor 1, room 104): informal presentation by Guillaume Chevillon (Prof., Essec). Jan. 28, 6pm, La Défense EEE (Cnit floor 1, room 201): seminar by Sir David F. Hendry (Nuffield College, Oxford), Empirical Model Discovery. Jan. 21, 12:30pm, La Défense EEE (Cnit floor 1, room 104): seminar by Michel M. Dacorogna (Dr, Head of SCOR Group Financial Modeling), There will be a next crisis surprising us
someday – how can we be prepared to survive it? 1st Term: Dec. 17, 12pm, La Défense EEE (amphi 138): seminar by Arthur Charpentier (Prof., Univ. Rennes 1 & Ecole Polytechnique), Extremes and Dependence in the context of Solvency II for Insurance Companies. Dec. 3, 8:30am: conference RISK (Risk Intelligence Symposium & Knowledge) organized by OTC Conseil & Univ. Paris Ouest; Caisse des dépôts et consignations – Paris. Nov. 19, 10am, N305 (campus Cergy): informal presentation by Fernando Oliveira (Prof., Essec) Nov.3 (Tuesday), 11:30am, Le Club (campus Cergy): seminar by Fabrice Cavarretta (Prof., Essec), Distinguishing Extreme vs. Average Effects in Nascent Firms: an Organizational Risk approach to resources. Oct. 29, 10am, N305 (campus Cergy): discussion on the objectives of this working group |
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