The Basel Advanced Measurement Approach requires financial institutions to compute capital requirements on internal data sets. In this paper we introduce a new methodology permitting capital requirements to take into account the embedded dependence structures of operational risks. The loss...

We investigate some statistical properties of the new k-factor Gegenbauer process with heteroscedastic noises One of the goals of the paper is to give tools which permit to use this model to explain the behaviour of certain data sets in finance and in macroeconomics. Monte Carlo experiments are...

This paper presents a 2-regime SETAR model with a long-memory process in the first regime and a short-memory process in the second regime. We briefly introduce the properties of this model and methods for locating the threshold parameter are proposed. Such a process is applied to stock indices...

We consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regurlarly random vatiables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process are regularly varying with tail exponent. We...

We investigate the asymptotic behavior of the maxima of a general class of deterministic chaotic processes –including the Tent map and the Logistic map -, of noisy chaotic processes, and of the Gaussian long memory k-factor Genebauer processes.

Using Archimedean copulas, we investigate the dependence structure existing between several series of financial assets log-returns that come from different markets. These series are considered as components of a portfolio and they are investigated on a long period including high shocks. To...

In this paper we discuss different aspects of long memory behaviorand applicable parametric models. We discuss the confusion thatcan arise when the empirical autocorrelation function decreasesin an hyperbolic way.

In this paper, we compre the time fresuency deconvolution method with the wavelets method. We apply our results on several dynamical systems and show the capability of the wavelet's method to reconstruct the attractor of a chaotic time series? We de-noise different data sets in order to rebuilt...

This paper introduces non-parametric estimators for upper and lower tail dependence whose confidence intervals are obtained with a bootstrap method. We call these estimators "Naïve estimators" as they represent a discretization of Joe's formulae (1997)\nocite{Joe} linking copulas to tail...

For a GARCH(1,1) process, we study the large deviation asymptotics at the horizon k and their consequences for extreme quantile estimation. The results are relevant for the estimation of multi-period Value at Risk and prove that the heuristic “square k” rule used in financial risk management...