CHORRO Christophe

Finding causal relationships in large dimensional systems is of key importance in a number of fields. Granger non-causality tests have become standard tools, but they only detect the direction of the causality, not its strength. To overcome this point, in the frequency domain, several measures have been introduced such as the Direct Transfer Function (DTF), the Partial Directed Coherence measure (PDC) or the Generalized Partial Directed Coherence measure (GPDC). Since these measures are based on a two-step estimation, consisting in i) estimating a Vector AutoRegressive (VAR) in the time domain and ii) using the VAR coefficients to compute measures in the frequency domain, they may suffer from cascading errors. Indeed, a flawed VAR estimation will translate into large biases in coherence measures. Our goal in this paper is twofold. First, using Monte Carlo simulations, we quantify these biases. We show that the two-step procedure results in highly inaccurate coherence measures, mostly due to the fact that non-significant coefficients are kept, especially in parsimonious systems. Based on this idea, we next propose a new methodology (mBTS-TD) based on VAR reduction procedures, combining the modified-Backward-in-Time selection method (mBTS) and the Top-Down strategy (TD). We show that our mBTS-TD method outperforms the classical two-step procedure. At last, we apply our new approach to recover the topology of a weighted financial network in order to identify through the local directed weighted clustering coefficient the most systemic assets and exclude them from the investment universe before allocating the portfolio to improve the return/risk ratio.

No summary available.

No summary available.

No summary available.

No summary available.

In 2003, Nicolas Bouleau published Error Calculus for Finance and Physics, The language of Dirichlet Forms, the fruit of two decades of research in the field of stochastic analysis and applied mathematics, with the objective of proposing a mathematically rigorous and operational approach to the handling of errors (in measurement or modeling) and their propagation. Published in the Nouvelle Bibliothèque Mathématique collection, this new book takes the challenge of making this fertile field of research accessible to a much wider public. This challenge is, in particular from a pedagogical point of view, amply successful. The reading of this book will satisfy both the undergraduate and graduate student, familiar with Differential Calculus and elementary probability theory, who wishes to apply his theoretical knowledge to applications, and the experienced modeler who wishes to develop a rigorous and critical engineering of his models. Finally, the researcher will find in this book material to think about the powerful Dirichlet theory of forms from an original angle. This book is composed of 5 parts with a strong emphasis on examples and applications.

In this paper, we discuss the pricing performances of a large collection of GARCH models by questioning the global synergy between the choice of the affine/non-affine GARCH specification, the use of competing alternatives to the Gaussian distribution, the selection of an appropriate pricing kernel and the choice of different estimation strategies based on several sets of financial information. Furthermore, the study answers an important question in relation to the correlation between the performance of a pricing scheme and its ability to forecast VIX dynamics. VIX analysis clearly appears as a parsimonious first-stage filter to discard the worst GARCH option pricing models.

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimization problem. Our study is based on the case of the Maximum Variety Portfolio and may be obviously extended to other classical frameworks with analogous results. We focus on the fact that the assets should preferably be classified in homogeneous groups before applying the proposed methodology which is to whiten the data before estimating the covariance matrix using the robust Tyler M-estimator and the Random Matrix Theory (RMT). The proposed procedure is applied and compared to standard techniques on real market data showing promising improvements.

No summary available.

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimization problem. The particular case of the Maximum Variety Portfolio is treated but the same improvements apply also in the other optimization problems such as the Minimum Variance Portfolio. We assume that the most important information (or the latent factors) are embedded in correlated Elliptical Symmetric noise extending classical Gaussian assumptions. We propose here to focus on a recent method of model order selection allowing to efficiently estimate the subspace of main factors describing the market. This non-standard model order selection problem is solved through Random Matrix Theory and robust covariance matrix estimation. Moreover we extend the method to non-homogeneous assets returns. The proposed procedure will be explained through synthetic data and be applied and compared with standard techniques on real market data showing promising improvements.

This article questions the empirical usefulness of leverage effects to forecast the dynamics of equity returns. In sample, we consistently find a significant but limited contribution of leverage effects over the past 25 years of S&P 500 returns. From an out-of-sample forecasting perspective and using a variety of different models, we find no statistical or economical value in using leverage effects, provided that an asymmetric and fat-tailed conditional distribution is used. This conclusion holds both at the index level and for 70% of the individual stocks constituents of the equity index.

The extraction of the jump component in dynamics of asset prices haw witnessed a considerably growing body of literature. Of particular interest is the decomposition of returns' quadratic variation between their continuous and jump components. Recent contributions highlight the importance of this component in forecasting volatility at different horizons. In this article, we extend a methodology developed in Maheu and McCurdy (2011) to exploit the information content of intraday data in forecasting the density of returns at horizons up to sixty days. We follow Boudt et al. (2011) to detect intraday returns that should be considered as jumps. The methodology is robust to intra-week periodicity and further delivers estimates of signed jumps in contrast to the rest of the literature where only the squared jump component can be estimated. Then, we estimate a bivariate model of returns and volatilities where the jump component is independently modeled using a jump distribution that fits the stylized facts of the estimated jumps. Our empirical results for S&P 500 futures, U.S. 10-year Treasury futures, USD/CAD exchange rate and WTI crude oil futures highlight the importance of considering the continuous/jump decomposition for density forecasting while this is not the case for volatility point forecast. In particular, we show that the model considering jumps apart from the continuous component consistenly deliver better density forecasts for forecasting horizons ranging from 1 to 30 days.

In this paper we consider some elementary and fair zero-sum games of chance to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties. From a mathematical perspective, we interestingly recover for small and high-frequency transactions some diffusion limits extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms.

No summary available.

This article questions the empirical usefulness of leverage effects to describe the dynamics of equity returns. Relying on both in and out of sample tests we consistently find a weak contribution of leverage effects over the past 25 years of S&P 500 returns. The skewness in the conditional distribution of the returns's time series models in found to explain most of the returns' distribution's asymmetry. This conclusion holds both at the index level and for 70% of the individual stocks constituents of the equity index.

We propose in the present paper a probabilistic approach of the so-called Hayes (2002) Yard-Sale model using classical diffusion approximations of Markov chains. We partly recover, at the very least for small and high frequency transactions, recent results of Boghosian (2014a) and Boghosian et al. (2015) concerning both wealth condensation in the absence of redistribution mechanisms and steady state distributions when a uniform capital taxation is imposed.

Since the stagflation observed following the sharp rise in the price of oil in 1973 and 1979, oil shocks have been considered one of the most potentially important sources of fluctuations in the United States as well as in many industrialized countries. Many articles have studied the role of oil shocks in the fluctuation of the main macroeconomic variables, namely growth, unemployment, inflation and wages. However, this work has not yet led to a consensus. The debate has even intensified over the past decade, due to a lack of a strong response from the real economy during the period of rising oil prices between 2002 and 2007. In effet, the recession that such a price increase should have caused was not observed until the subprime crisis in 2008. Several hypotheses were put forward to explain the difference between the crises of the 1970s and 2000s. Blanchard & Gali (2009) and Blanchard & Riggi (2013) mention, for example, the reduction in the amount of oil used in production, greater flexibility in real wages and greater credibility of monetary policy. Hamilton (2009) and Kilian (2008), on the other hand, suggest that it can be explained by the different origins of the two oil shocks: a supply shock during the 1970s and a demand shock during the 2000s. The original objective of the thesis was to re-examine the impact of oil shocks on the real economy through the debt channel. [The development of this work initiated in the thesis may lead to an alternative modeling framework that is decisive for the intelligence of macroeconomics. It should allow a better understanding of the evaluation of the reciprocal relations between the financial sphere, the reality of real macroeconomic cycles, energy and climate in what is undoubtedly the challenge of our generation: the ecological transition.

Empirical and theoretical studies have attempted to establish the U-shape of the log-ratio of conditional risk-neutral and physical probability density functions. The main subject of this paper is to question the use of such a U-shaped pricing kernel to improve option pricing performances. Starting from the so-called Inverse Gaussian GARCH model (IG-GARCH), known to provide semi-closed form formulas for classical European derivatives when an exponential affine pricing kernel is used, we build a new pricing kernel that is non-monotonic and that still has this remarkable property. Using a daily dataset of call options written on the S&P500 index, we compare the pricing performances of these two IG-GARCH models proving, in this framework, that the new exponential U-shaped stochastic discount factor clearly outperforms the classical exponential affine one. What is more, several estimation strategies including options or VIX information are tested taking advantage of the analytical tractability of these models.

No summary available.

In this paper we consider some elementary and fair zero-sum games of chance to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties, in particular, we underscore that randomness plays a key role in concentrating the wealth to the extreme with a single player. From a mathematical perspective, we interestingly recover for small and high-frequency transactions some diffusion limits extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms. We show that taxation of income is not sufficient to overcome the externe concentration process contrary to a uniform taxation of capital that stabilizes the economy preventing agents to be ruined.

We propose in the present paper a probabilistic approach of the so-called Hayes (2002) Yard-Sale model using classical diffusion approximations of Markov chains. We partly recover, at the very least for small and high frequency transactions, recent results of Boghosian (2014) and Boghosian et al. (2015) concerning both wealth condensation in the absence of redistribution mechanisms and steady state distributions when a uniform capital taxation is imposed.

No summary available.

No summary available.

No summary available.

No summary available.

No summary available.

No summary available.

Since the end of 2008, my research work has gradually turned towards problems related to financial econometrics. More precisely, the aim was to incorporate in classical GARCH models probability laws capable of taking into account the phenomena of asymmetry and leptokurticity that can be observed in most financial series. The inclusion of these two stylized facts in GARCH models is fundamental both for improving the predictive power of the models (forecasting) and for the valuation of derivatives (pricing). The abandonment of the Gaussian hypothesis is however not without consequences.

Lévy processes and their applications in finance.