Siegel détermina un domaine fondamental à l'aide de la réduction de Minkowski des formes quadratiques. Il donna tous les détails concernant ce domaine pour le genre 1. C'est la détermination du domaine fondamental de Minkowski présentée comme deuxième condition et la condition maximal height présentée comme troisième condition, qui empêchent la précision exacte de ce domaine pour le cas général. Les derniers résultats ont été obtenus par Gottschling pour le genre 2 en 1959. Elle est depuis restée inexplorée et mal comprise notamment les différents domaines de Minkowski. Afin d'identifier ce domaine fondamental pour le genre 3, nous présentons des résultats concernant sa troisième condition. Chaque fonction abélienne peut être écrite en termes de fonctions rationnelles des fonctions thêta et de leurs dérivées. Cela permet l'expression de la solution des systèmes intégrables en fonction des fonctions thêta. Ces solutions sont pertinentes dans la description de surfaces de vagues d'eau, de l'optique non linéaire. Deconinck et Van Hoeij ont éveloppé et mis en oeuvre des algorithmes pour construire la matrice de Riemann et Deconinck et al. ont développé le calcul des fonctions thêta correspondantes. Deconinck et al. ont utilisé l'algorithme de Siegel pour atteindre approximativement le domaine fondamental de Siegel et ont adopté l'algorithme LLL pour trouver le vecteur le plus court. Alors que nous utilisons ici un nouvel algorithme de réduction de Minkowski jusqu'à dimension 5 et une détermination exacte du vecteur le plus court pour des dimensions supérieures. / Siegel determined a fundamental domain using the Minkowski reduction of quadratic forms. He gave all the details concerning this domain for genus 1. It is the determination of the Minkowski fundamental domain presented as the second condition and the maximal height condition, presented as the third condition, which prevents the exact determination of this domain for the general case. The latest results were obtained by Gottschling for the genus 2 in 1959. It has since remained unexplored and poorly understood, in particular the different regions of Minkowski reduction. In order to identify Siegel's fundamental domain for genus 3, we present some results concerning the third condition of this domain. Every abelian function can be written in terms of rational functions of theta functions and their derivatives. This allows the expression of solutions of integrable systems in terms of theta functions. Such solutions are relevant in the description of surface water waves, non linear optics. Because of these applications, Deconinck and Van Hoeij have developed and implemented al-gorithms for computing the Riemann matrix and Deconinck et al. have developed the computation of the corresponding theta functions. Deconinck et al. have used Siegel's algorithm to approximately reach the Siegel fundamental domain and have adopted the LLL reduction algorithm to nd the shortest lattice vector. However, we opt here to use a Minkowski algorithmup to dimension 5 and an exact determination of the shortest lattice vector for greater dimensions.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22231号 / 理博第4545号 / 新制||理||1653(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 池田 保, 教授 雪江 明彦, 教授 並河 良典 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The master thesis is looking into the estimation of yield curve using two ap- proaches. The first one is searching for parametric model which is able to describe the behavior of yield curve well and estimate its parameters. The parametric mo- dels used in the thesis are derived from the class of models introduced by Nelson and Siegel. The second approach is nonparametric estimation of yield curves using spline smoothing and kernel smoothing. All used methods are then compared on real observed data and their suitability for various tasks and concrete available observations is considered. 1

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19548号 / 理博第4208号 / 新制||理||1604(附属図書館) / 32584 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 池田 保, 教授 雪江 明彦, 准教授 市野 篤史 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22968号 / 理博第4645号 / 新制||理||1668(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 市野 篤史, 教授 池田 保, 教授 加藤 周 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this study, four frequently used yield curve construction methods are evaulated on a set of metrics with the aim of determining which method is the most suitable for estimating yield curves from European zero rates. The included curve construction methods are Nelson-Siegel, Nelson-Siegel-Svensson, cubic spline interpolation and forward monotone convex spline interpolation. We let the methods construct yield curves on multiple sets of zero yields with different origins. It is found that while the interpolation methods show greater ability to adapt to variable market conditions as well as hedge arbitrary fixed income claims, they are outperformed by the parametric methods regarding the smoothness of the resulting yield curve as well as their sensitivity to noise and perturbations in the input rates. This apart from the Nelson-Siegel method's problem of capturing the behavior of underlying rates with a high curvature. The Nelson-Siegel-Svensson method did also exhibit instability issues when exposed to perturbations in the input rates. The Nelson-Siegel method and the forward monotone convex spline interpolation method emerge as most favorable in their respective categories. The ultimate selection between the two methods must however take the application at hand into consideration due to their fundamentally different characteristics. / I denna studie utvärderas fyra välanvända metode för att konstruera yieldkurvor på ett antal punkter. Detta med syfte att utröna vilken metod som är bäst lämpad för att estimera yieldkurvor på Europeiska nollkupongräntor. Metoderna som utvärderas är Nelson-Siegel, Nelson-Siegel-Svensson, cubic spline-interpolering samt forward monotone convex spline-interpolering. Vi låter metoderna estimera yieldkurvor på flera sammansättningar nollkupongräntor med olika ursprung. Vi ser att interpoleringsmetoderna uppvisar en större flexibilitet vad gäller att anpassa sig till förändrade marknadsförutsättningar samt att replikera godtyckliga ränteportföljer. När det gäller jämnhet av yieldkurvan och känsligheten för brus och störningar i de marknadsräntor som kurvan konstrueras utifrån så presterar de parametiska metoderna däremot avsevärt bättre. Detta bortsett från att Nelson-Siegel-metoden hade problem att fånga beteendet hos nollkupongräntor med hög kurvatur. Vidare hade Nelson-Siegel-Svensson-metoden problem med instabilitet när de underliggande marknadsrentorna utsattes för störningar. Nelson-Siegen-metoden samt foward monotone convex spline-interpolering visade sig vara bäst lämpade för att konstruera yieldkurvor på de Europeiska marknaderna av de utvärderade metoderna. Vilken metod av de två som slutligen bör användas behöver bedömas från fall till fall grundat i vilken tillämpning som avses.

Submitted by Ulisses Nehmi (ulisses@nehmi.com.br) on 2017-12-22T17:42:27Z No. of bitstreams: 1 Dissert_MPE_Ulisses_2017.12.pdf: 2808696 bytes, checksum: fe4dbd86f710e7d09cbb1705853aba42 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2017-12-22T17:51:45Z (GMT) No. of bitstreams: 1 Dissert_MPE_Ulisses_2017.12.pdf: 2808696 bytes, checksum: fe4dbd86f710e7d09cbb1705853aba42 (MD5) / Made available in DSpace on 2017-12-23T15:56:54Z (GMT). No. of bitstreams: 1 Dissert_MPE_Ulisses_2017.12.pdf: 2808696 bytes, checksum: fe4dbd86f710e7d09cbb1705853aba42 (MD5) Previous issue date: 2017-12-15 / Muitos estudos sobre a Estrutura a Termo das Taxas de Juros (ETTJ) focam na análise de um único país, geralmente uma economia desenvolvida. São raros os estudos que avaliam as características das curvas de juros para um conjunto de países desenvolvidos, e ainda mais raros os estudos que avaliam essas características para países emergentes. Este estudo parametrizou a ETTJ de 19 economias por um período de 10 anos, divididas entre economias desenvolvidas e emergentes, identificando as principais características que definem cada grupo, algumas das quais se revelaram contraintuitivas. A parametrização das curvas de juros também foi utilizada para remover o ruído dos dados originais, o que permitiu uma análise mais precisa dos fatores que explicam suas variâncias. Com isso, foram encontradas evidências de diferenças relevantes no peso dos fatores nível, inclinação e curvatura na explicação das variações na ETTJ para os países desenvolvidos em relação aos países emergentes. / Many studies on Term Structure of Interest Rates (TSIR) focus on the analysis of a single country, usually a developed economy. Seldom do studies evaluate the features of yield curves for a set of developed countries, and even more rarely do studies evaluate these features for emerging countries. The present study evaluates the parametric TSIR of 19 economies over a period of 10 years, grouped into two distinct sets: developed and emerging economies. It identifies the main features, some of which have proved counterintuitive, that define each group. The parameterization of the yield curves was also used to removed noise from the original data, which allowed for a more accurate analysis of the factors that explain its variances. Evidence of relevant differences in weights for the level, slope and curvature factors were found, which explain the variations in the TSIR of developed countries relative to emerging countries.

Submitted by Juliane Andrade (juliane.a.andrade@gmail.com) on 2018-09-25T12:53:53Z No. of bitstreams: 1 DissertacaoFinalJulianeAndrade.pdf: 2648304 bytes, checksum: 0feea2eb88019ffdafb37180bd261f3b (MD5) / Approved for entry into archive by Joana Martorini (joana.martorini@fgv.br) on 2018-09-25T15:17:07Z (GMT) No. of bitstreams: 1 DissertacaoFinalJulianeAndrade.pdf: 2648304 bytes, checksum: 0feea2eb88019ffdafb37180bd261f3b (MD5) / Approved for entry into archive by Suzane Guimarães (suzane.guimaraes@fgv.br) on 2018-09-25T16:40:46Z (GMT) No. of bitstreams: 1 DissertacaoFinalJulianeAndrade.pdf: 2648304 bytes, checksum: 0feea2eb88019ffdafb37180bd261f3b (MD5) / Made available in DSpace on 2018-09-25T16:40:46Z (GMT). No. of bitstreams: 1 DissertacaoFinalJulianeAndrade.pdf: 2648304 bytes, checksum: 0feea2eb88019ffdafb37180bd261f3b (MD5) Previous issue date: 2018-08-16 / Esse trabalho apresenta análise combinada entre a macroeconomia e a estrutura a termo das taxas de juros, através de duas modelagens distintas. Primeiramente, utiliza-se o modelo Novo Keynesiano de pequeno porte, que é combinado com o modelo dinâmico de Nelson-Siegel. Em seguida estima-se o modelo dinâmico de Nelson-Siegel integrado com variáveis macroeconômicas. São empregados dados mensais referentes aos contratos futuros de DI, de Setembro de 2002 a Dezembro de 2017. A comparação das modelagens mostra que o modelo combinado apresenta resultados mais consistentes do que o modelo integrado. / This paper aims to present a combined analysis between macroeconomics and the term structure of interest rates, through two different models. Firstly, a small New Keynesian model is used, which is combined with the dynamic Nelson-Siegel model. Then the NelsonSiegel dynamic model integrated with macroeconomic variables is estimated. Monthly data on DI futures contracts are used from September 2002 to December 2017. Comparison of modeling shows that the combined model presents more consistent results than the integrated model.

Submitted by Camilo de Léllis Cavalcanti Júnior (camilojr@gmail.com) on 2013-09-20T14:38:32Z No. of bitstreams: 1 Dissertação - Estratégia de Trading Utilizando o Modelo Dinâmico de Nelson-Siegel Final.pdf: 1310470 bytes, checksum: f90849f3305d9519f30ddd197d650214 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-09-20T14:43:47Z (GMT) No. of bitstreams: 1 Dissertação - Estratégia de Trading Utilizando o Modelo Dinâmico de Nelson-Siegel Final.pdf: 1310470 bytes, checksum: f90849f3305d9519f30ddd197d650214 (MD5) / Made available in DSpace on 2013-09-20T14:49:57Z (GMT). No. of bitstreams: 1 Dissertação - Estratégia de Trading Utilizando o Modelo Dinâmico de Nelson-Siegel Final.pdf: 1310470 bytes, checksum: f90849f3305d9519f30ddd197d650214 (MD5) Previous issue date: 2013-08-21 / Esta pesquisa busca testar a eficácia de uma estratégia de arbitragem de taxas de juros no Brasil baseada na utilização do modelo de Nelson-Siegel dinâmico aplicada à curva de contratos futuros de taxa de juros de 1 dia da BM&FBovespa para o período compreendido entre 02 de janeiro de 2008 e 03 de dezembro de 2012. O trabalho adapta para o mercado brasileiro o modelo original proposto por Nelson e Siegel (1987), e algumas de suas extensões e interpretações, chegando a um dos modelos propostos por Diebold, Rudebusch e Aruoba (2006), no qual estimam os parâmetros do modelo de Nelson-Siegel em uma única etapa, colocando-o em formato de espaço de estados e utilizando o Filtro de Kalman para realizar a previsão dos fatores, assumindo que o comportamento dos mesmos é um VAR de ordem 1. Desta maneira, o modelo possui a vantagem de que todos os parâmetros são estimados simultaneamente, e os autores mostraram que este modelo possui bom poder preditivo. Os resultados da estratégia adotada foram animadores quando considerados para negociação apenas os 7 primeiros vencimentos abertos para negociação na BM&FBovespa, que possuem maturidade máxima próxima a 1 ano. / This research tries to test the effectiveness of an interest rate arbitrage strategy in Brazil based on a Dynamic Nelson-Siegel model applied to the term structure of future contracts of 1 day of interest rates traded at BM&FBovespa for the time between January, 2nd of 2008, and December, 3rd, 2012. The work adapts to the Brazilian market the mode originally proposed by Nelson and Siegel (1987), and some of its extensions and interpretations, reaching one of the models proposed by Diebold, Rudebusch and Aruoba (2006), in which they estimate the parameters of Nelson-Siegel Model in one only step, putting it in a state-space form and using the Kalman Filter to make the factors’ forecast, assuming that their behavior is an order 1 VAR. The model has the advantage that all the parameters are estimated simultaneously, and the authors showed that it has a good forecast power. The results of the adopted strategy were encouraging when considered for negotiation only the 7 first available maturities at BM&FBovespa, which have maturity of around 1 year.

L'objectif de cette thèse est de fournir à la Banque Audi des outils économétriques et appliqués pour une gestion des risques plus efficace et plus robuste. Les banques libanaises sont aujourd'hui confrontées à des défis plus importants que jamais: l'avenir de la région Moyen-Orient repose sur les conséquences de la guerre civile syrienne. Dans ce contexte, la gestion des taux d'intérêt et de la liquidité s'avère de plus en plus compliqué pour les banques commerciales. En premier lieu, le risque de taux d'intérêt sur le marché libanais sera étudié. Ce marché est connu pour son manque de liquidité et le problème de calibrage des modèles de taux est difficile. Afin de résoudre ce problème, nous utilisons les prix historiques des obligations émises par le gouvernement libanais et libellées en monnaie locale et en dollars américains. Nous considérons des modèles de Nelson-Siegel et Svensson et contraignons le niveau corrélation des facteurs pour stabiliser l'estimation des paramètres de ces modèles. La méthode conduit à des résultats qui s'interprètent très facilement d'un point de vue économique et peuvent être utilisés pour la prévision des variations de la courbe des taux en se basant une analyse ´économique prospective. En second lieu, la problématique des dépôts des clients traditionnels sera étudiée. Ces derniers sont reconnus comme étant la source principale de financement des banques commerciales libanaises (80-85% du passif). Bien qu'ils soient contractuellement des dépôts à court terme (principalement un mois) versant des taux d'intérêt fixes, ces dépôts sont assimilés à une source de financement stable possédant un comportement proche des taux d'intérêt du marché. Nous développons un modèle à correction d'erreur représentant un équilibre à long terme entre le Libor et le taux moyen du secteur bancaire libanais offert sur les dépôts en dollars américains. Les résultats permettent de déterminer une date de réévaluation des dépôts clientèles en cas de fluctuation des taux d'intérêt. Une nouvelle duration du passif tenant compte des comportements des clients a été mise en place. Elle sera par construction plus élevée que la duration contractuelle. En cas de hausse des taux d'intérêt, une baisse de l'écart entre la duration des actifs et des passifs sera alors observée menant à la diminution de l'impact négatif de la hausse. Après avoir étudié le profil de risque des taux des dépôts clientèles, nous commençons la deuxième partie de la thèse par la détermination de l'échéancier des retraits. Nous segmentons les données historiques des données sur les dépôts clientèles selon: la monnaie, le type de dépôt et la résidence du déposant. Pour chaque filtre, un modèle `a correction d'erreur est développé. Les résultats montrent la relation entre les dépôts clientèles, un indicateur relatif du niveau économique et les écarts entre les taux offerts sur le marché libanais. Ainsi, le modèle permettra d'évaluer le comportement des retraits des dépôts clientèles et de comprendre leur profil de risque de liquidité. Les grandes institutions financières détiennent des positions importantes en actifs financiers. La dernière partie de la thèse discute de la gestion du risque de liquidité de marché en cas de session forcée de ces actifs. Nous supposons qu'un investisseur détient une position importante d'un actif donné, à t = 0, un choc sévère provoque une forte dépréciation de la valeur de l'actif et par conséquent, force l'investisseur à opter pour la liquidation du portefeuille dès que possible en limitant ses pertes. Les rendements des actions sont modélisés par des processus de type GARCH qui sont adaptés pour décrire des comportements extrêmes suite à une grande variation de l'actif au temps initial. Suivant que le marché est liquide ou illiquide, nous proposons une stratégie optimale à l'investisseur qui maximise sa fonction d'utilité. Enfin, nous intégrons dans le modèle un avis d'expert pour optimiser la prise d'une décision / The aim of this thesis is to provide Bank Audi with econometric tools for sake of a more robust risk management. Lebanese businesses today are faced with greater challenges than ever before, both economical and political, and there is a question about the future of the middle east region after the Syrian civil war. Thus, Lebanese commercial banks face greater complications in the management of interest rate and liquidity risk. The first part of this thesis discusses interest rate risk management and measurement in the Lebanese market. First, we seek to build the Lebanese term structure. This market is known by its illiquidity, yields for a given maturity make a large jump with a small impact on other yields even if close to this maturity. Therefore, we face challenges in calibrating existing yield curve models. For this matter, we get historical prices of bonds issued by the Lebanese government, and denominated in Local currency and in US dollar. A new estimation method has been added to Nelson Siegel and Svensson model, we call it “Correlation Constraint Approach”. Model parameters can be interpreted from economical perspective which will be helpful in forecasting yield curve movements based on economist’s opinion. On the second hand, traditional customer deposits are the main funding source of Lebanese commercial banks (80-85% of liabilities). Although they are contractually short term (mainly one month) paying fixed interest rates, these deposits are historically known to be a stable source of funding and therefore exhibit a sticky behavior to changes in market interest rates. We develop an error correction model showing a long-run equilibrium between Libor and Lebanese banking sector average rate offered on USD deposits. Results make it possible to determine the behavioral duration (repricing date) of customer deposits when market interest rates fluctuate. Therefore, the behavioral duration of liabilities will be higher than the contractual one which will lower the duration gap between assets and liabilities and thus the negative impact of positive interest rate shocks. After understanding interest risk profile of customers’ deposits, we start the second part by determining their behavioral liquidation maturity. We get Bank Audi’s historical deposits outstanding balances filtered into the following categories: currency, account typology and residency of depositor. We develop an error correction model for each filter. Results show relationship between deposits behaviors, the coincident indicator and spreads between offered rates in the Lebanese market. The model will lead to assess behavioral liquidation maturity to deposits and understand their liquidity risk profile. This will be helpful for the funding liquidity risk management at Bank Audi. Large financial institutions are supposed to hold large positions of given assets. The last topic is related to market liquidity risk management. We suppose an investor holds a large position of a given asset. Then at time 0, a severe shock causes a large depreciation of the asset value and makes the investor decides to liquidate the portfolio as soon as possible with limited losses. Stock returns are modeled by GARCH process which has tail behaviors after large variation at time 0. Trading on liquid and illiquid markets, we provide the trader with best exit trading strategy maximizing his utility function, finally we incorporate into the model an expert opinion which will help the investor in taking the decision