Jules Sadefo Kamdem

VaR and ES for Linear Portfolios with Mixture of Generalized Laplace Distributions Risk Factors

In this paper, we propose an explicit estimation of Value-at-Risk (VaR) and Expected Shortfall (ES) for linear portfolios when the risk factors change with a convex mixture of generalized Laplace distributions (M-GLD). We introduce the dynamics Delta-GLD-VaR, Delta-GLD-ES, Delta-MGLD-VaR and Delta-MGLD-ES, by using conditional correlation multivariate GARCH. The generalized Laplace distribution impose less restrictive assumptions during estimation that should improve the precision of the VaR and ES through the varying shape and fat tails of the risk factors in relation with the historical sample data. We also suggested some areas of application to measure price risk in agriculture, risk management and financial portfolio optimization.

Generalized Integral Transforms with the Homotopy Perturbation Method

This paper applies He’s homotopy perturbation method to compute a large variety of integral transforms. The Esscher, Fourier, Hankel, Laplace, Mellin and Stieljes integrals transforms are particular cases of our generalized integral transform. Our method is of practical importance in order to derive new integration formulae, to approximate certain difficult integrals as well as to calculate the expectation of certain nonlinear functions of random variable.This paper applies He’s homotopy perturbation method to compute a large variety of integral transforms. The Esscher, Fourier, Hankel, Laplace, Mellin and Stieljes integrals transforms are particular cases of our generalized integral transform. Our method is of practical importance in order to derive new integration formulae, to approximate certain difficult integrals as well as to calculate the expectation of certain nonlinear functions of random variable.

Time-Frequency Analysis of the Relationship Between EUA and CER Carbon Markets

In this paper, interactions or co-movement between the CER and EUA futures prices are examined in order to shed light on the dependency between the European Union Emissions Trading Scheme (EU ETS) and the clean development mechanism (MDP). Our analysis uses the wavelet method to model the correlation between CER and EUA in the time-frequency domain. It highlights the impact of different investors (according to their investment horizons) on the co-movement between the CER and EUA prices, and therefore, the behavior of individual investors as speculators, arbitrageurs, and hedgers on European allowance and CDM credits cumulatively. In this vein, we analyze according to the frequency intervals, price convergence, identification of potential factors that could explain a difference in futures prices, and structural changes in the EUA and CER prices. The application is made using daily EUA’s and CER’s prices data.

Hedge Funds Risk-adjusted Performance Evaluation: A Fuzzy Set Theory-Based Approach

The hedge funds performance evaluation requires an adequate characterization of returns distributions shape. This characterization is made by thorough probabilistic moments. Different types of moments were used in the literature, namely, the conventional (central or raw) moments (Sharpe, 1966, Treynor and Black, 1973), the partial moments (Sortino and van der Meer, 1991, Sortino, van der Meer and Platinga, 1999, Bernardo and Ledoit, 2000, Sortino and Satchel, 2001, Farinelli and Tibiletti, 2008) and more recently the Trimmed L-moments (Darrolles et al., 2009). These authors generally define the performance ratio by dividing a location measure by a dispersion measure. The seminal approach deriving from the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), Mossin (1966) and Treynor (1962) uses the sample mean and the standard deviation of excess returns as location and dispersion measures respectively. These two statistics do not always adequately describe the returns distributions, especially in the presence of heavy tails and/or of skewness.