Essay on the State of Research and Innovation in France and the European Union

Innovation in the economy is an important engine of growth and no economy, whatever its complexity and degree of advancement, whether it is based on industry, agriculture, high tech or the providing of services, can be truly healthy without innovating actors within it. The aim of this work, done by an applied mathematician working in finance, not by an economist or a lawyer, isn't to provide an exhaustive view of the all the mechanisms in France and in Europe that aim at fostering innovation in the economy and to offer solutions for removing all the roadblocks that still hinder innovation; indeed such a study would go far beyond the scope of this study. What I modestly attempted to achieve in this study was firstly to draw a panorama of what is working and what needs to perfected as far as innovation is concerned in France and Europe, then secondly to offer some solutions and personal thoughts to boost innovation.Comment: 26 pages. Modifications in the new version : Reference [7] was invalid (it was a report that was never voted and published by the French Senate, contrary to what I assumed) and has been replaced. The corresponding part has been modified in consequence. Also, minor correction

A Pratical Approach to Financial Crisis Indicators Based on Random Matrices

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2015.49 - ISSN : 1955-611XThe aim of this work is to build financial crisis indicators based on market data time series. After choosing an optimal size for a rolling window, the market data is seen every trading day as a random matrix from which a covariance and correlation matrix is obtained. Our indicators deal with the spectral properties of these covariance and correlation matrices. Our basic financial intuition is that correlation and volatility are like the heartbeat of the financial market: when correlations between asset prices increase or develop abnormal patterns, when volatility starts to increase, then a crisis event might be around the corner. Our indicators will be mainly of two types. The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix. As reference distribution we will use the theoretical Marchenko Pastur distribution and, mainly, simulated ones using a random matrix of the same size as the empirical rolling matrix and constituted of Gaussian or Student-t coefficients with some simulated correlations. The idea behind this first type of indicators is that when the empirical distribution of the spectrum of the covariance matrix is deviating from the reference in the sense of Hellinger, then a crisis may be forthcoming. The second type of indicators is based on the study of the spectral radius and the trace of the covariance and correlation matrices as a mean to directly study the volatility and correlations inside the market. The idea behind the second type of indicators is the fact that large eigenvalues are a sign of dynamic instability.Le but de ce travail de recherche est la construction d'indicateurs de crises financières basés sur des données de marché. Après avoir choisi la taille optimale d'une fenêtre roulante, les données de marchés seront vues comme une matrice aléatoire à partir de laquelle une matrice de covariance et une matrice de corrélation seront obtenues. Nos indicateurs exploitent les propriétés spectrales de cette matrice de covariance et de cette matrice de corrélation. Notre intuition financière de base est que la corrélation et la volatilité sont le pouls d'un marché financier : quand les corrélations entre les actifs augmentent ou développent des comportements anormaux, quand la volatilité commence à augmenter, alors un évènement de crise est peut être sur le point de se produire. Nos indicateurs seront essentiellement de deux types. Le premier type est basé sur la distance de Hellinger, calculée entre la distribution des valeurs propres de la matrice de covariance empirique et la distribution des valeurs propres d'une matrice de covariance de référence. Comme distribution de référence nous utiliserons la distribution théorique de Marchenko Pasur et aussi, essentiellement, des distributions simulées en utilisant une matrice aléatoire de même taille que la matrice de covariance roulante empirique et constituée de coefficients suivant une loi Gaussienne ou t-student et présentant des corrélations. L'idée derrière ce premier type d'indicateurs est que quand la distribution empirique du spectre de la matrice de covariance commence à dévier au sens de Hellinger de la référence, alors une crise est probablement sur le point de se produire. Le second type d'indicateurs est basé sur l'étude du rayon spectral et de la trace de la matrice de covariance et de la matrice de corrélation, dans le but d'étudier directement la volatilité et la corrélation à l'intérieur du marché. L'idée derrière ce second type d'indicateurs est que de grandes valeurs propres sont un signe d'instabilité dynamique

Indicateurs de crises financières et applications aux stratégies de trading algorithmique

This thesis is constituted of three research papers and is articulated around the construction of financial crisis indicators, which produce signals, which are then applied to devise successful systematic trading strategies. The first paper deals with the establishment of a framework for the construction of our financial crisis indicators. Their predictive power is then demonstrated by using one of them to build an active protective-put strategy, which is able to beat in terms of performance a passive strategy as well as, most of the time, multiple paths of a random strategy. The second paper goes further in the application of our financial crisis indicators to the elaboration of systematic treading strategies by using the aggregated signal produce by many of our indicators to govern a portfolio constituted of a mix of cash and ETF shares, replicating an equity index like the SP500. Finally, in the third paper, we build financial crisis indicators by using a completely different approach. By studying the dynamics of the evolution of the distribution of the spreads of the components of a CDS index like the ITRAXX Europe 125, a Bollinger band is built around the empirical cumulative distribution function of the distribution of the spreads, fitted on a basis constituted of two lognormal distributions, which have been chosen beforehand. The crossing by the empirical cumulative distribution function of either the upper or lower boundary of this Bollinger band is then interpreted in terms of risk and enables us to construct a trading signal.Cette thèse, constituée de trois papiers de recherche, est organisée autour de la construction d’indicateurs de crises financières dont les signaux sont ensuite utilisés pour l’élaboration de stratégies de trading algorithmique. Le premier papier traite de l’établissement d’un cadre de travail permettant la construction des indicateurs de crises financière. Le pouvoir de prédiction de nos indicateurs est ensuite démontré en utilisant l’un d’eux pour construire une stratégie de type protective-put active qui est capable de faire mieux en termes de performances qu’une stratégie passive ou, la plupart du temps, que de multiples réalisations d’une stratégie aléatoire. Le second papier va plus loin dans l’application de nos indicateurs de crises à la création de stratégies de trading algorithmique en utilisant le signal combiné d’un grand nombre de nos indicateurs pour gouverner la composition d’un portefeuille constitué d’un mélange de cash et de titres d’un ETF répliquant un indice equity comme le SP500. Enfin, dans le troisième papier, nous construisons des indicateurs de crises financières en utilisant une approche complètement différente. En étudiant l’évolution dynamique de la distribution des spreads des composantes d’un indice CDS tel que l’ITRAXXX Europe 125, une bande de Bollinger est construite autour de la fonction de répartition de la distribution empirique des spreads, exprimée sur une base de deux distributions log-normales choisies à l’avance. Le passage par la fonction de répartition empirique de la frontière haute ou de la frontière basse de cette bande de Bollinger est interprétée en termes de risque et permet de produire un signal de trading

Winning Investment Strategies Based on Financial Crisis Indicators

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail-du-ces/Documents de travail du Centre d'Economie de la Sorbonne 2017.39 - ISSN : 1955-611XThe aim of this work is to create systematic trading strategies built upon several financial crisis indicators based on the spectral properties of market dynamics. Within the limitations of our framework and data, we will demonstrate that our systematic trading strategies are able to make money, not as a result of pure luck but, in a reproducible way and while avoiding the pitfall of over fitting, as a result of the skill of the operators and their understanding and knowledge of the financial market. Using singular value decomposition (SVD) techniques in order to compute all spectra in an efficient way, we have built two kinds of financial crisis indicators with a demonstrable power of prediction. Firstly, there are those that compare at every date the distribution of the eigenvalues of a covariance or correlation matrix to a distribution of reference representing either a calm or agitated market reference. Secondly, we have those that merely compute at every date a chosen spectral property (trace, spectral radius or Frobenius norm) of a covariance or correlation matrix. Aggregating the signals provided by all the indicators in order to minimize false positive errors, we then build systematic trading strategies based on a discrete set of rules governing the investment decisions of the investor. Finally, we compare our active strategies to a passive reference as well as to random strategies in order to prove the usefulness of our approach and the added value provided by the out-of-sample predictive power of the financial crisis indicators upon which our systematic trading strategies are built

Indicateurs de crises financières et applications aux stratégies de trading algorithmique

Cette thèse, constituée de trois papiers de recherche, est organisée autour de la construction d’indicateurs de crises financières dont les signaux sont ensuite utilisés pour l’élaboration de stratégies de trading algorithmique. Le premier papier traite de l’établissement d’un cadre de travail permettant la construction des indicateurs de crises financière. Le pouvoir de prédiction de nos indicateurs est ensuite démontré en utilisant l’un d’eux pour construire une stratégie de type protective-put active qui est capable de faire mieux en termes de performances qu’une stratégie passive ou, la plupart du temps, que de multiples réalisations d’une stratégie aléatoire. Le second papier va plus loin dans l’application de nos indicateurs de crises à la création de stratégies de trading algorithmique en utilisant le signal combiné d’un grand nombre de nos indicateurs pour gouverner la composition d’un portefeuille constitué d’un mélange de cash et de titres d’un ETF répliquant un indice equity comme le SP500. Enfin, dans le troisième papier, nous construisons des indicateurs de crises financières en utilisant une approche complètement différente. En étudiant l’évolution dynamique de la distribution des spreads des composantes d’un indice CDS tel que l’ITRAXXX Europe 125, une bande de Bollinger est construite autour de la fonction de répartition de la distribution empirique des spreads, exprimée sur une base de deux distributions log-normales choisies à l’avance. Le passage par la fonction de répartition empirique de la frontière haute ou de la frontière basse de cette bande de Bollinger est interprétée en termes de risque et permet de produire un signal de trading.This thesis is constituted of three research papers and is articulated around the construction of financial crisis indicators, which produce signals, which are then applied to devise successful systematic trading strategies. The first paper deals with the establishment of a framework for the construction of our financial crisis indicators. Their predictive power is then demonstrated by using one of them to build an active protective-put strategy, which is able to beat in terms of performance a passive strategy as well as, most of the time, multiple paths of a random strategy. The second paper goes further in the application of our financial crisis indicators to the elaboration of systematic treading strategies by using the aggregated signal produce by many of our indicators to govern a portfolio constituted of a mix of cash and ETF shares, replicating an equity index like the SP500. Finally, in the third paper, we build financial crisis indicators by using a completely different approach. By studying the dynamics of the evolution of the distribution of the spreads of the components of a CDS index like the ITRAXX Europe 125, a Bollinger band is built around the empirical cumulative distribution function of the distribution of the spreads, fitted on a basis constituted of two lognormal distributions, which have been chosen beforehand. The crossing by the empirical cumulative distribution function of either the upper or lower boundary of this Bollinger band is then interpreted in terms of risk and enables us to construct a trading signal

An empirical approach to financial crisis indicators based on random matrices

International audienceThe aim of this work is to build a class of financial crisis indicators based on the spectral properties of the dynamics of market data. After choosing an appropriate size for a rolling window, the historical market data inside this rolling window are seen every trading day as a random matrix from which a correlation matrix is obtained. Our goal is to study the correlations between the assets that constitute this market and look for reproducible patterns that are indicative of an impending financial crisis. A weighting of the assets in the market is then introduced and is proportional to the daily traded volumes. This manipulation is realized in order to give more importance to the most liquid assets. Our financial crisis indicators are based on the spectral radius of this weighted correlation matrix. The idea behind this type of financial crisis indicators is that large eigenvalues are a sign of dynamic instability. The out-of-sample predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective put strategy

Stochastic Evolution of Distributions - Applications to CDS indices

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2017.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2017.07 - ISSN : 1955-611XWe use mixture of percentile functions to model credit spread evolution, which allows to obtain a flexible description of credit indices and their components at the same time. We show regularity results in order to extend mixture percentile to the dynamic case. We characterise the stochastic differential equation of the flow of cumulative distribution function and we link it with the ordered list of the components of the credit index. The main application is to introduce a functional version of Bollinger bands. The crossing of bands by the spread is associated with a trading signal. Finally, we show the richness of the signals produced by functional Bollinger bands compared with standard one with a pratical example

A Case Study of the Impact of Climate Change on Agricultural Loan Credit Risk

Changing weather patterns may impose increased risk to the creditworthiness of financial institutions in the agriculture sector. To reduce the credit risk caused by climate change, financial institutions need to update their agricultural lending portfolios to consider climate change scenarios. In this paper we introduce a framework to compute the optimal agricultural lending portfolio under different increased temperature scenarios. In this way we quantify the impact of increased temperature, taken as a measure of climate change, on credit risk. We provide a detailed case study of how our approach applies to the problem of optimizing a portfolio of agricultural loans made to corn farmers across different corn producing regions of Ontario, Canada, under various climate change scenarios. We conclude that the lending portfolio obtained by taking into account the climate change is less risky than the lending portfolio neglecting climate change.Science, Irving K. Barber Faculty of (Okanagan)Non UBCComputer Science, Mathematics, Physics and Statistics, Department of (Okanagan)ReviewedFacult

A Case Study of the Impact of Climate Change on Agricultural Loan Credit Risk

Changing weather patterns may impose increased risk to the creditworthiness of financial institutions in the agriculture sector. To reduce the credit risk caused by climate change, financial institutions need to update their agricultural lending portfolios to consider climate change scenarios. In this paper we introduce a framework to compute the optimal agricultural lending portfolio under different increased temperature scenarios. In this way we quantify the impact of increased temperature, taken as a measure of climate change, on credit risk. We provide a detailed case study of how our approach applies to the problem of optimizing a portfolio of agricultural loans made to corn farmers across different corn producing regions of Ontario, Canada, under various climate change scenarios. We conclude that the lending portfolio obtained by taking into account the climate change is less risky than the lending portfolio neglecting climate change