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Published Papers, Working Papers and Presentations in Conferences

Mind the Solvency II Gap: A Coherent Measure of Market Consistent Embedded Value to Interest Rate Risk in ALM
This paper derives Asset and Liability Management (“ALM”) interest rate risk measures (i.e. duration and convexity gaps) applicable to Life insurance companies that are adequate such as asset and liability-driven strategies can be used within a mix of tactics and instruments to achieve financial objectives, for a given set of ALM interest rate risk indicator tolerances. The approach adopted relies on a half-way approach between immunization (i.e. duration match) and dedication (i.e. cash flows match) that consists to match both the duration and convexity of the market value of assets and best estimate liabilities as well as the inclusion of partial and key-rate duration and convexity matches. The recent changes in regulation through the adoption of a market consistent framework (i.e. MCEV) combined to distressed economic conditions with failing equity markets, brutal changes in interest rates and spreads further increase the motivation for a rigorous and coherent definition of ALM risk measures in order to manage appropriately interest rate risk of Life insurance companies. Through this paper, effective and key-rate duration (and convexity) gaps are derived based on the interpretation of ALM risk indicators as approximation of interest rate sensitivities within a market consistent framework. Those concepts are discussed with respect to their usefulness for ALM of Life insurance companies. This paper is of high interest in the context of Solvency II given the lack of guidelines provided by EIOPA regarding the treatment and management of interest rate risk from an ALM perspective.
Asset and Liability Management (ALM), interest rate risk, Market Consistent Embedded Value (MCEV), duration, convexity, duration gap, convexity gap, key-rate duration, key-rate convexity, immunization, dedication, half-way approach, target duration, convexity impact, stochastic ALM, Dynamic Financial Analysis (DFA)
Reinterpretation of Solvency Capital Requirements through an Analytical Formula
In the context of Solvency II, insurance companies access and manage economic capital across various techniques requiring generally heavy Monte Carlo simulation procedures in order to derive an appropriate loss distribution. However, very little attention has been addressed to model Solvency Capital Requirements (SCR) based on the derivation of a closed-form formula. While the current industry standard is to make use of sophisticated algorithms requiring a significant calculation time given the current state-of-the-art computer technology and the amount of computational resources required for some techniques such as the stochastic-in-stochastic valuation that is particularly difficult to implement in practice for large participating Life insurance portfolios, a flexible and realistic modeling structure is proposed. This paper explores a convenient and straightforward solution for quantifying economic capital that aims at investigating notably the limited attempt that has been addressed so far at modeling economic capital via an adequate closed-form formula. The analytical formula proposed has the advantage of avoiding the use of simplified approaches such as the replicating portfolio for instance that has been largely criticized for its poor ability to replicate appropriately liabilities without introducing a significant error in the loss distribution covering against market risk. This paper contradicts the recent trend of highly complex modeling frameworks developed by some insurance companies for producing economic capital that can be hardly produced with high frequency and is in clear opposition with directives provided in CEIOPS, [4]. We aim to support the idea of developing a type of partial internal model allowing to better know the risks an insurance company is exposed to while keeping the attractive advantage of a closed-form solution. The approach adopted shows that SCR can be obtained based on the knowledge of systematic risks and conditional moments of order 1 and 2 of the distribution of net cash flows. An explicit solution for SCR is provided based on the derivation of a partial internal economic capital model that is general and flexible enough to further assess SCR via the inclusion of various assumptions largely detailed in this paper and allows to refine the approach. The attractive features of the modeling structure are its analytical formula, accuracy and encompass the interactions between assets and liabilities. Importantly, from our belief, the proposed modeling structure appears in accordance with CEIOPS, [5], the general principles that aim to ensure a harmonized approach to the use of internal models throughout insurance companies.
Solvency Capital Requirements, SCR, Solvency II, Analytical Formula, Economic Capital, Partial Internal Model
A Formalized Hybrid Portfolio Replication Technique Applied to Participating Life Insurance Portfolios
The practice of portfolio replication has proven its applicability to market risk management in complete markets through the appropriate modeling of a range of non-linear financial instruments. Replicating portfolios provide an intuitive and operational framework for explaining financial risks of life insurance comapnies as financial instruments with analytical formulae encompassing instruments’ non-linearities, path dependency and specific sensitivities capture financial risks. Carrying out the market risk calculation for life insurance companies requires the replicating portfolio technique as the plan calculation referred to as ‘stochastic in stochastic’ requires immense computational power. For each of the real-world scenarios, the market-consistent values of assets and liabilities on the basis of the replicating portfolio technique are therefore determined. This article presents an enhanced replicating portfolio framerwork that is of utmost importance for the generation of market risk capital requirements applied to life insurance portfolios embedding options and guarantees. While the classic replication technique requires approximations and expert judgments as there is no clear-cut, easy answer for finding an optimal replicating portfolio providing a superior replication power (i.e. a portfolio composed of a finite number of financial vanilla instruments in an arbitrage-free context out of which the cash-flows best replicate the magnitude and timing of liabilities over the projection term), the proposed approach relies on a formalized framework that leads to build optimal replicating portfolios for participating life insurance business. This paper derives the principles behind the portfolio replication technique and provides explanations and justifications on the parameterization of replicating portfolios via a practical application case. The approach adopted is a hybrid model that combines a “pure” portfolio replication technique and the curve fitting approach. As a result, the quality of replicating portfolios in extreme capital market environments is tested by means of a comparison with the results of a brute force revaluation incorporating a large range of sensitivities such as EEV, QIS 5 and extreme scenario (close to the economic capital driven scenario) sensitivities. In order to determine the weights of financial instruments, the ordinary least square technique is used to find the best possible portfolio composition that replicates liability cash flows in several market conditions at either the present or terminal value of the projection. Additional enhancement techniques such as a particular adjustment within the singular value decomposition and a scenario filter are introduced to better fit the weights of selected instruments with liability moves. An example of calibration strategy that leads to an optimal replicating portfolio is broadly described in this paper.
Replicating Portfolio, European Embedded Value, Time Value of Options and Guarantees, Market-Consistent Valuation, Participating Life Insurance Portfolio, Market Risk Capital Requirements, Financial Vanilla Instrument, European-Style Instrument, Curve Fitting Technique, Ordinary Least Square Technique, Constraint Optimization, Lagrange Multiplier, Singular Value Decomposition, Scenario Filter
A Stochastic Model for Credit Spreads under a Risk-Neutral Framework through the use of an Extended Version of the Jarrow-Lando-Turnbull Model
 The model derives risky corporate bond prices (or equivalently credit spreads) subject to credit default and migration risk, based on an extended version of the Jarrow, Lando and Turnbull model, under a risk-neutral framework, as a result of the simulation of a continuous time, time-homogeneous Markov chain. The inclusion of credit default and migration risk is made possible due to an allowance for a credit risk premium that varies stochastically. While the standard Jarrow-Lando-Turnbull model assumes that the credit risk premium is a deterministic function of time which, along with the assumption of a constant “real-world” transition matrix and constant recovery rate, leads to deterministic credit spreads, the extension proposed through this article captures a stochastic risk premium in order to better fit with historical observation. The model is of particular importance in the European Embedded Value (i.e. EEV) context where risk-neutral scenarios are required for calculating the Time Value of Options and Guarantees (i.e. TVOG) covering all material options and guarantees embedded following the requirements of EEV principles. Moreover, the model can also be used in a real-world framework for pricing government and risky corporate debts with the exclusion of the Markov chain. This allows to capture the marginal impact of credit default and migration risk at the TVOG level due to the corresponding changes that arise on the economic scenarios. The methodology is applied to corporate debts, but the extension proposed is flexible enough to be applicable to other securities as well. 
bond pricing, stochastic credit spreads, enhanced Jarrow, Lando and Turnbull model, risk-neutral valuation, Markov chain, arbitrage-free condition, European Embedded Value, Time Value of Options and Guarantees
Enhanced Valuation of European Options under Jump Processes and Innovative Characterization of Implied Volatility Smile
 An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical trackability of the Black-Scholes model. The main advantage of this model is to lie on a consistent framework that does not make stringent assumptions in order to derive a closed-form option pricing formula and to capture rare events such as major political changes or catastrophic events through the use of discontinuous stochastic processes. Moreover, this model does not much face any calibration issue given that little dependence with non-observable parameters is introduced. Moreover, an innovative quantification of pricing differences is proposed between the in-house (i.e. the own made pricing formula including jumps) and the classic Black-Scholes model through implied volatility and its curve resembles a smile, meaning that the introduction of jumps is quantified via a smile according to implied volatility. In order to derive such an implied volatility smile, an iterative search procedure referred to as the Newton-Raphson algorithm is proposed. Numerical experiments of both the in-house pricing formula and its implied volatility recursive algorithm are presented and results show that both the two are fast computing via computers through the use of coding languages.
option pricing, enhanced model, European call, jump, Poisson-driven process, Black-Scholes, Merton, implied volatility, volatility smile, closed-form solution, Newton-Raphson recursive algorithm
Review of Econometric Models Applicable to Hedge Fund Returns Capturing Serial Correlation and Illiquidity
Hedge Fund returns are often highly serially correlated mainly due to illiquidity exposures given that investments in such securities tend to be inactively traded and associated market prices are not always readily available. Following that, observed returns of such alternative investments tend to be smoother than “true” unobserved returns, which, in fact, turn out to underestimate risk measures such as volatility (i.e. standard deviation). In order to encompass for such serial correlation and illiquidity, we propose three econometric models. The first model referred to as the log-normally distributed random walk model with time varying parameters is largely used in the risk industry for Value-at-Risk purposes. Its main goal, in our context, is to derive specific characteristics of Hedge Fund returns by challenging and invalidating its assumptions (i.e. log-normality assumption and presence of autocorrelation between returns as well as their squares). The next two, referred to as the Blundell-Ward and the Getmansky, Lo and Markarov model respectively, both encompass an unsmoothing process and incorporate a predictive model for volatility. However, their mathematical background lies on a diametrically different perspective. Last but not the least, we propose for both an adequate model extension (i.e. a Markov-switching model for Blundell-Ward and conditional serial correlation for Getmansky, Lo and Markarov) that provide a superior volatility forecasting given the limitations arising within their actual standard mathematical formalism.
Hedge Funds, random walk model, Blundell-Ward model,Getmansky, Lo and Markarov model, serial correlation, smoothing, illiquidity, volatility forecasting, EWMA, ”square root of time” relationship, Markov-switching model, conditional serial correlation
Credit Risk Modeling Through the use of an Extended and Numerically Stable Version of CreditRisk+ and a Merton Model
Accessing and managing credit risk has been a major area of interest and concern for both academics, practitioners and regulators, particularly in the afterwards of the recent 2008 financial crisis. Moreover, the effective management of credit risk is a challenge faced by any banking and insurance companies, and a critical success factor for a strong embedded Enterprise Risk Management. In this paper, we propose a model that mimics actuarial mathematics in order to describe credit risk in a portfolio including the modeling of both credit default risk and credit migration risk The credit default risk model can be described as an extended version of the CreditRisk+ model using both the Panjer recursion and the Fourier transform through an idiosyncratic risk factor and various systematic risk factors in order to adequately derive a probability density function for losses. The generated distribution is equivalent to a convolution of a large number of Gamma-Poisson mixtures. The main innovation is to separately derive a loss distribution for each risk factor with the Panjer recursion allowing to analyze the idiosyncratic or systematic risk supported by any risk factor and then, to use the attractive feature of complex numbers, via the Fourier transform, to determine an appropriate global loss distribution for credit default risk. The algorithm is based on both actuarial sciences and numerical mathematics and turns out to be particularly useful for analyzing very large credit portfolios by accurately capturing the tail and the body of the loss distribution for credit default risk. The main advantage is to ensure a numerically stable computation for credit default risk avoiding the well-know round-off error that accumulates in the original version of the generalized CreditRisk+ model. From our knowledge, this mixed algorithm was not published so far. In addition of both the Value-at-Risk and Expected Shortfall measurement, we computed the Value-at-Risk contribution per exposure that can be of major interest for business making decision and introduced a Markow process to quantify credit migration risk based on an extended Merton model. The attractive feature of both models is that only a few inputs are required to perform well and no assumptions are made on the default event so that the model can be easily extended to some risk categories such as operational risk where no attempts are made on the causes of default or migration for quantifying an economic capital.
credit risk, credit default risk, credit migration risk, credit portfolio modeling, CreditRisk+, Markov process, Merton model, transition matrix model, Value-at-Risk, Expected Shortfall, Value-at-Risk contribution, Panjer recursion, Fourier transform, operational risk
Calibration of Credit Spread Scenarios for Monte Carlo Simulations
The main goal of this paper is to better understand the behavior of credit spreads in the past and the potential risk of unexpected future credit spread changes. One important consideration to note regarding credit spreads is the fact that bond spreads contain a liquidity premium, which compensates for the risk that the bond cannot be sold at fair value due to a lack of liquidity in the market. As the Credit Default Swap (CDS) market demonstrates more liquidity, CDS spreads are a good proxy for credit spreads excluding the liquidity premium. As a result, this paper presents a set of spread shocks derived from both CDS and bond markets in order to capture spread risk excluding or including a liquidity premium in the aforementioned markets. An empirical study demonstrates that an obvious liquidity premium exists between the bond market and the CDS market. Next, an economic study quantifying the appropriate level of spread shocks is examined. Following this, a stochastic model simulated by the Monte Carlo technique including a mean reverting property, a jump process and a predictive model for the volatility is proposed to forecast credit spreads across rating classes. Then, a methodology allowing to transform a non-positive definite correlation matrix into the nearest positive definite correlation matrix is derived. Finally, this paper provides a methodology for computing the marginal spread risk factor contribution applicable to any type of risk factors derived from the Monte Carlo Value-at-Risk method, and offers a practical implementation of Quasi Monte Carlo, a form of low discrepancy sequences offering shorter computational times associated to a higher accuracy than Monte Carlo.
Fonds Souverains: Chevaliers Blancs ou Prédateurs? Les fonds souverains représent-t-ils une menace ou une opportunité pour la stabilité du système financier mondial?
Les fonds souverains ne sont pas un phénomène nouveau. Leur existence remonte à plus de 50 ans. Cependant, leur importance au sein de la finance mondiale a pris une ampleur considérable ces dernières années. D’autre part, les évènements récents liés à la crise financière les ont propulsés au devant de la scène internationale. En 2007, les investissements publiquement enregistrés faits par ces fonds ont atteints 92 milliards de dollars contre seulement 3 milliards de dollars en 2000. L’objectif de ce mémoire est de mettre en évidence l’impact des fonds souverains sur la stabilité du système financier mondial. Ont-ils une influence notable ou au contraire s’agit-il d’acteurs de second rang ? Peuvent-ils jouer un rôle de stabilisateur des marchés financiers ou au contraire apportent-ils d’avantage d’instabilités ? Les actions engagées par ces fonds lors de la récente crise financière ont-elles été source de stabilisation ?
Keywords
fonds souverains, excédants de la balance commerciale, système financier mondial, stratégie de développement, déséquilibres structurels, fonds opaques, “sauveur“ d’établissements financiers, “l’après-pétrole“, excédents d’avoir de réserve, prédateurs, services de macro-couverture, guerre d’accumulation
Un Modèle à Changement de Régime Markovien Applicable à la Prédiction de l’Indice Boursier S&P 500
L'objectif de ce mémoire est de prévoir l'évolution de l’indice boursier S&P 500 à l’aide d’un modèle à changement de régime Markovien. Une approche didactique est utilisée au travers ce document apportant une place prépondérantes à certaines notions fondamentales d’économétrie. Premièrement, une description très précise de la série temporelle est fournie ainsi que les motivations qui ont conduites à choisir l’indice S&P 500. Deuxièmement, une statistique descriptive est appliquée conduisant à déterminer les caractéristiques intrinsèques de la série étudiée. Les tests de stationnarité ainsi que divers tests d'hypothèses tels que l'hypothèse de normalité permettent de définir un modèle approprié pour modéliser la série temporelle. Notons qu'une procédure très détaillée des tests de stationnarité est fournie. Troisièmement, le modèle ARMA le plus approprié est déterminé. De plus, l'étude des résidus permet de déterminer un modèle adéquate pour la volatilité à l'aide d'une représentation autorégressive de la variance conditionnelle du processus (modèle de type GARCH). Quatrièmement, une modélisation sous forme de régime Markovien est adoptée. Plus précisément, deux modèles autorégressifs représentant chacun un état particulier sont déterminés. Cette forme de représentation est tout à fait adaptée à l'étude d'un indice boursier puisqu'il convient généralement de dériver deux modèles reflétant un modèle d'expansion et de crise respectivement. Dans le cadre de notre étude, l'utilisation d'une telle approche permet de mettre en évidence l'existence d'un régime à faible volatilité et un second à forte volatilité. Le calcul associé des probabilités filtrées (filtre d’Hamilton) puis lissées (lisseur de Kim) permettent de déterminer dans quel état le processus évolue à l'aide de l'utilisation de modèles de séries temporelles à changement de régime Markovien d'ordre 1. L’objectif de cette partie étant de déterminer les prévisions de probabilités d’être dans un état connaissant l’ensemble des informations passées et présents ainsi que d’identifier les paramètres de notre série temporelle (volatilité, corrélation, moyenne) en maximisant le calcul de vraisemblance. La dérivation d'un modèle approprié de prévision de l'indice S&P 500 découle de ces probabilités filtrées et des paramètres estimés pour chacun des deux modèles utilisés. Le calcul de probabilités filtrées fait appel au filtre d'Hamilton utilisant un processus autorégressif à deux retards. Ce filtre est tout d’abord utilisé dans le cadre d'une modélisation à deux régimes, puis à trois régimes afin de produire une estimation a priori plus fine. Enfin, une prévision pour l'instant t+1 est fournie ainsi que pour plusieurs intervalles futures à l'aide d'une approche itérative en réinjectant la prévision obtenue dans les données initiales, recalculant l'ensemble des probabilités filtrées et en appliquant un calcul d'espérance pour la détermination de la prévision. Une analyse des résultats obtenus permet de déterminer dans quel état la prévision se situe (période d’expansion ou de crise). 
Keywords
prévision de l'indice boursier S&P 500, modèle à changement de régime Markovien d'ordre 1, ARMA, volatilité, GARCH, tests de stationarité, filtre d'Hamilton, lisseur de Kim, probabilités filtrées, probabilités lissées, tests d'hypothèses, régime à faible volatilité, régime à forte volatilité, économétrie

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