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Introduction

## Publications

Publications (44)

This paper investigates the optimal asset allocation of a financial institution whose customers are free to withdraw their capital-guaranteed financial contracts at any time. In accounting for the asset-liability mismatch risk of the institution, we present a general utility optimization problem in a discrete-time setting and provide a dynamic prog...

We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. For this purpose, we use a specific type of regression model on an augmented dataset of lagged time series. Our model is inspired by dynamic regression models (Pankratz 2012), with the response...

In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of associated adaptive robust Bellman equation. The success of our appro...

Yield curve interpolation and extrapolation using no arbitrage short rates models

The performance of portfolio managers is usually assessed by comparing their allocation strategies to a benchmark portfolio. A major issue for portfolio managers of liability driven institutions is that no benchmark is given to them, although they face mid-term objectives with short term constraints. No performance attribution methodology may then...

Due to the lack of reliable market information, building financial term-structures may
be associated with a significant degree of uncertainty. In this paper, we propose a new
term-structure interpolation method that extends classical spline technics by additionally
allowing for quantification of uncertainty. The proposed method is based on a genera...

In this paper, we study the statistical estimation of some factor credit migration models, that is, multivariate migration models for which the transition matrix of each obligor is driven by the same dynamic factors. In particular, we compare the statistical estimation of the ordered Probit model as described for instance in Gagliardini and Gourier...

In the past decade, Sobol's variance decomposition have been used as a tool -
among others - in risk management. We show some links between global
sensitivity analysis and stochastic ordering theories. This gives an argument
in favor of using Sobol's indices in uncertainty quantification, as one
indicator among others.

We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-step procedure, much like in a standard static copula setup....

In this paper, we analyze the diversity of term structure functions (e.g.,
yield curves, swap curves, credit curves) constructed in a process which
complies with some admissible properties: arbitrage-freeness, ability to fit
market quotes and a certain degree of smooth- ness. When present values of
building instruments are expressed as linear combi...

In this paper, we introduce two alternative extensions of the classical univariate Conditional-Tail-Expectation (CTE) in a multivariate setting. The two proposed multivariate CTE are vector-valued measures with the same dimension as the underlying risk portfolio. As for the multivariate Value-at-Risk measures introduced in Cousin and Di Bernardino...

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas t...

Let X = (X1;X2;X3) be a three-dimensional correlated Brownian motion and T i be the first hitting time of a fixed level by Xi. The purpose of this paper is to compute the joint density of T = inf(T1, T2, T3) and X_T . We prove that the method of images used in dimension two by Iyengar leads us to a tiling three-dimensional space problem. A such a p...

We consider a bottom-up Markovian copula model of {portfolio} credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula s...

In "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model", the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part...

In this paper, we prove that the conditional dependence structure of default times in the Markov model of "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective" belongs to the class of Marshall-Olkin copulas. This allows us to derive a factor representation in terms of "common-shocks", the latter being able to trigg...

The present paper provides a multi-period contagion model in the credit risk field. Our model
is an extension of Davis and Lo’s infectious default model. We consider an economy of n firms
that may default directly or may be infected by other defaulting firms (a domino effect also
being possible). Spontaneous defaults without external influence and...

In this paper, we consider the hedging of portfolio loss derivatives using single-name credit default swaps as hedging instruments. The hedging issue is investigated in a general pure jump dynamic setting where default times are assumed to admit a joint density. In a first step, we compute default intensities adapted to the global filtration of def...

Pricing of Portfolio Credit DerivativesFactor Models for the Pricing of CDO TranchesA Review of Factor Approaches to the Pricing of CDOsConclusion

We investigate a dynamic credit risk contagion model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by conditionally independent Bernoulli-type random variables. We pr...

In this paper, we introduce a multivariate extension of the classical
univariate Value-at-Risk (VaR). This extension may be useful to understand how
solvency capital requirement is affected by the presence of risks that cannot
be diversify away. This is typically the case for a network of highly
interconnected financial institutions in a macro-prud...

In this paper, we introduce two alternative extensions of the classical
univariate Value-at-Risk (VaR) in a multivariate setting. The two
proposed multivariate VaR are vector-valued measures with the same
dimension as the underlying risk portfolio. The lower-orthant VaR is
constructed from level sets of multivariate distribution functions
whereas t...

ISBN-10: 8847023416, ISBN-13: 978-8847023413

While the Gaussian copula model is commonly used as a static quotation device for CDO tranches, its use for hedging is questionable.
In particular, the spread delta computed from the Gaussian copula model assumes constant base correlations, whereas we show
that the correlations are dynamic and correlated to the index spread. It might therefore be e...

We present in this paper the actuarial Waring formula, which is used in several fields, like life-insurance or credit risk. In a particular framework where considered random variables are exchangeable, we show that some problems can occur when using this formula. We propose alternative recursions in order to improve the complexity of the calculatio...

This chapter intends to provide insights about the topical issue of risk managing synthetic collateralized debt obligations (CDOs). We stand in the gray zone between mathematical finance and financial econometrics, between academic and market practitioners' approaches. We chose to first present two scholar models, each of them leading to perfect re...

In this article we study a decoupled forward backward stochastic differential equation (FBSDE) and the associated system of partial integro-differential obstacle problems, in a flexible Markovian set-up made of a jump-diffusion with regimes. These equations are motivated by numerous applications
in financial modeling, whence the title of the paper....

This set of lecture notes is concerned with the following pair of ideas and concepts:
1.
The Skorokhod Embedding problem (SEP) is, given a stochastic process X=(X
t
)
t≥0 and a measure μ on the state space of X, to find a stopping time τ such that the stopped process X
τ has law μ. Most often we take the process X to be Brownian motion, and μ to...

These lecture notes cover a major part of the crash course on financial modeling with jump processes given by the author in
Bologna on May 21–22, 2009. After a brief introduction, we discuss three aspects of exponential Lévy models: absence of arbitrage,
including more recent results on the absence of arbitrage in multidimensional models, propertie...

In this first chapter, we show that a CDO tranche payoff can be perfectly replicated with a self-financed strategy based on
the underlying credit default swaps. This extends to any payoff which depends only upon default arrivals, such as basket default
swaps. Clearly, the replication result is model dependent and relies on two critical assumptions....

This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-Michel Lasry. This course was based
upon the articles of the three authors and upon unpublished materials they developed. Proofs were not presented during the
conferences and are now available. So are some issues that were only rapidly tackled during class.

We describe a replicating strategy of CDO tranches based upon dynamic trading of the corresponding credit default swap index. The aggregate loss follows a homogeneous Markov chain associated with contagion effects. Default intensities depend upon the number of defaults and are calibrated onto an input loss surface. Numerical implementation can be c...

Nous présentons une extension du modèle de Davis et Lo (2001).

This paper is a primer on the hedging and the risk management of CDO tranches. It intends to provide a global perspective on the current issues and refers to research papers for modelling and mathematical details. Though the basics of the risk management within the Gaussian copula model are not discussed, we review some issues which may eventually...

This paper is dedicated to risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of t...

This paper is dedicated to risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti's theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of t...

The recent liquidity crisis on the credit derivative market has raised the need for consistent mark-to-model valuation method for some exotic products such as leverage super-senior tranches. Roughly speaking, a Leverage Super-Senior (LSS) tranche is a path-dependent option on the market-value of a traditional super-senior tranche. This option is ex...

## Projects

Project (1)

Build, simulate, predict kriging model using inequality constraints like monotonicity, convexity and boundedness. Kriging model is similar to DiceKriging.
available online at https://github.com/maatouk/constrKriging
Authors: Hassan Maatouk and Yann Richet