This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric...

We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numéraire as an asset to trade in, we show how self-financed...

The discounting of very long-term cash-flows is crucial for the valuation oflong-term investment projects. In this paper, we analyze the market prices ofUS government bonds with very long-term time-to-maturity, and emphasizesome statistical specificities of very long-term zero-coupon rates, that...

We consider a kernel-based approach to nonlinear canonical correlation analysis and its implementation for time series. We deduce a test procedure of the reversibility hypothesis. The method is applied to the analysis of stochastic differential equation from high-frequency data on stock returns.

We decompose a stationary Markov process (Xt) as a linear combination of ARMA. These decompositions are deduced from a nonlinear canonical decomposition of the joint distribution of (Xt, Xt−1).

Standard risk measures, such as the value-at-risk (VaR), or the expected shortfall, have to be estimated, and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on <italic>n</italic> observations of the profit...

In the first part of this thesis, we introduce a new methodology for stress-test exercises. Our approach allows to consider richer stress-test exercises, which assess the impact of a modification of the whole distribution of asset prices’ factors, rather than focusing as the common practices...

In a nonlinear framework, temporal dependence of time series is sensitive to transformations. The aim of this paper is to examine in detail the relationships between various forms of persistence and nonlinear transformations of stationary and nonstationary processes. We introduce the concept of...