Optimal Portfolio Allocation under Asset and Surplus VaR Constraints

In this paper we propose an approach to Asset Liability Management of various institutions, in particular insurance companies, based on a dual VaR constraint for the asset and the surplus. A key ingredient of this approach is a flexible modelling of the term structure of interest rates leading to an explicit formula for the returns of bonds. VaR constraints on the asset and on the surplus also take tractable forms, and graphical illustrations of the impact and of the sensitivity of these constraints are easily explicited in terms of various parameters: share of stocks, duration and convexity of the bonds on the asset and liability sides, expected return and volatility of the asset...Asset Liability Management, interest rates, Asset VaR constraint, Surplus VaR constraint, Optimal Portfolio.

Multi-Lag Term Structure Models with Stochastic Risk Premia.

The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.Discrete-time Affine Term Structure Models ; Stochastic Discount Factor, Gaussian VAR(p) processes ; Stochastic risk premia ; Moving Average or discrete-time HJM representations ; Exact Fitting of the currently-observed yield curve.

Switching VARMA Term Structure Models - Extended Version.

The purpose of the paper is to propose a global discrete-time modeling of the term structure of interest rates able to capture simultaneously the following important features : (i) an historical dynamics of the factor driving term structure shapes involving several lagged values, and switching regimes; (ii) a specification of the stochastic discount factor (SDF) with time-varying and regime dependent risk-premia; (iii) explicit or quasi explicit formulas for zero-coupon bond and interest rate derivative prices; (iv) the positivity of the yields at each maturity. The first family of models we develop is given by the Switching Autoregressive Normal (SARN) and the Switching Vector Autoregressive Normal (SVARN) Factor-Based Term Structure Models of order p. The second family of models we study is given by the Switching Autoregressive Gamma (SARG) and the Switching Vector Autoregressive Gamma (SVARG) Factor-Based Term Structure Models of order p. Regime shifts are described by a Markov chain with (historical) non-homogeneous transition probabilities.Affine Term Structure Models ; Stochastic Discount Factor ; Car processes ; Switching Regimes ; VARMA processes ; Lags ; Positivity ; Derivative Pricing.

Credit and liquidity risks in euro area sovereign yield curves

In this paper, we propose a model of the joint dynamics of euro-area sovereign yield curves. The arbitrage-free valuation framework involves five factors and two regimes, one of the latter being interpreted as a crisis regime. These common factors and regimes explain most of the fluctuations in euro-area yields and spreads. The regime-switching feature of the model turns out to be particularly relevant to capture the rise in volatility experienced by fixed-income markets over the last years. In our reduced-form set up, each country is characterized by a hazard rate, specified as some linear combinations of the factors and regimes. The hazard rates incorporate both liquidity and credit components, that we aim at disentangling. The estimation suggests that a substantial share of the changes in euro-area yield differentials is liquidity-driven. Our approach is consistent with the fact that sovereign default risk is not diversifiable, which gives rise to specific risk premia that are incorporated in spreads. Once liquidity-pricing effects and risk premia are filtered out of the spreads, we obtain estimates of the actual –or real-world– default probabilities. The latter turn out to be significantly lower than their risk-neutral counterparts.default risk, liquidity risk, term structure of interest rates, regime-switching, euro-area spreads.

Pricing and Inference with Mixtures of Conditionally Normal Processes.

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.

New Information Response Functions.

We propose a new methodology for the analysis of impulse response functions in VAR or VARMA models. More precisely, we build our results on the non ambiguous notion of innovation of a stochastic process and we consider the impact of any kind of new information at a given date $t$ on the future values of the process. This methodology allows to take into account qualitative or quantitative information, either on the innovation or on the future responses, as well as informations on filters. We show, among other results, that our approach encompasses several standard methodologies found in the literature, such as the orthogonalization of shocks (Sims (1980)), the "structural" identification of shocks (Blanchard and Quah (1989)), the "generalized" impulse responses (Pesaran and Shin (1998)) or the impulse vectors (Uhlig (2005)).Impulse response functions ; innovation ; new information.

Coherency Conditions In Simultaneous Linear Equation Models With Endogenous Switching Regimes

In modeling disequilibrium macroeconomic systems which one would want to subject to econometric estimation one typically faces the problem of whether the structural model can determine a unique equilibrium. The problem inherits a special form because the regimes in which the equilibria can lie are each linear. By placing restrictions on the parameters that insure the uniqueness of such a solution for each value of the exogenous and random variables, we can improve the estimation procedure. This paper provides necessary and sufficient conditions for uniqueness -- or "coherency." These conditions are applied to a variety of models that have been prominent in the literature on econometrics with 'switching regimes' such as those of self-selectivity (Maddala), simultaneous equation tobit and probit (Amemiya, Schmidt) and multi-market macroeconomic disequilibrium (Gourieroux, Laffont and Nonfort).

Taking into account extreme events in European option pricing.

According to traditional option pricing models,1 financial markets underestimate the impact of tail risk. In this article, we put forward a European option pricing model based on a set of assumptions that ensure, inter alia, that extreme events are better taken into account. Using simulations, we compare the option prices obtained from the standard Black and Scholes model with those resulting from our model. We show that the traditional model leads to an overvaluation of at-the-money options, which are the most traded options, while the less liquid in-the-money and out-of-the-money options are undervalued.

Quelques observations sur les grands mammifères du parc national de Tai (Cote d’Ivoire)

The Taï forest in Western Ivory Coast is the last sizeable refuge of a number of endemic Western African mammals, three of which being on the IUCN list of endangered species. Ten species of primates have so far been observed in this area : 2 prosimians, 3 species of guenons (Cercopithecus) , 3 spe cies of Colobus monkeys, one mangabey (Cercocebus) and the Chimpanzee. The Diana monkey is the most frequently observed species of guenons ; it often forms mixed troops with red, and black and white, colobus monkeys. Fifteen species of ungulates have been recorded, including pigmy hippopotamus, zebra duiker, Jenkink’s duiker and five other species of genus Cephalophus