Current economic situation is characterized for deflation and low inflation, low economic growth, and low or negative interest rates, which lead to phenomenon of issuing governments bonds with negative yield. The main goal of this work is to understand the valuation and behavior of bonds with condition of negative interest rates, analyze impacts of negative rates on volatility of bonds. This work also compares the behavior of negative yields of bonds in contrast with positive yields. The contribution of this work consists in the critical evaluation of limitations of the formula for calculating the bond price to fulfill its role if the values of negative interest rates are too low.

La théorie de l’utilité actualisée proposée par Samuelson (1937) est un des paradigmes dominants en économie et en gestion particulièrement en finance où elle sert de socle, entre autres, au Modèle Intertemporel d’Equilibre des Actifs (ICAPM) et à sa version incluant la consommation (ICCAPM). En dépit de cette place, sa validité pour expliquer les préférences temporelles des individus a été questionnée dans des travaux de recherche récents ouvrant la voie à des amendements et à la remise en cause de ce cadre d’analyse. Ces travaux ont introduit, entre autres, le concept de structure par terme du taux d’escompte psychologique. La littérature a proposé sept alternatives à la fonction d’escompte exponentielle contenue dans la version initiale de la théorie de l’utilité actualisée. Il s’agit des fonctions d’escompte de Hernstein, de Harvey, Proportionnelle, de Laibson, de Rachlin, Hyperbolique et Hyperbolique généralisée.Faisant suite à ces travaux, nous avons initié une recherche visant à apporter une réponse à la question relatives aux caractéristiques de la structure par terme du taux d’escompte psychologique d’un individu et les facteurs qui expliquent sa différence d’un individu à l’autre ; ses liens avec les autres dimensions des préférences (face au risque et sociales) individuelles sont explorés par la suite. Il s’est agi d’identifier parmi ces fonctions celles qui sont cohérentes avec les préférences individuelles observées, d’estimer les paramètres associés, d’étudier la cohérence des préférences temporelles d’un individu. Elle s’appuie sur les données issues d’une étude expérimentale basée sur dix huit arbitrages inter-temporels, quatre arbitrages de loteries, le jeu du dictateur, le jeu de l’ultimatum et le jeu de confiance.L’analyse des données a permis de confirmer les résultats précédents sur la violation de la constance du prix psychologique du temps, la cohérence par domaine des préférences temporelles, d’établir que la population étudiée est caractérisée par une hétérogénéité par rapport à la forme de la structure par terme du taux d’escompte psychologique. Les individus sont caractérisés par une fonction d’escompte psychologique de Hernstein, hyperbolique généralisée ou de Laibson. Nous avons trouvé que les caractéristiques démographiques, l’environnement social et l’orientation temporelle expliquent peu les différences de structure par terme de taux d’escompte psychologique. Les différences de niveaux d’application (dimension des traits de personnalités) sont les principaux déterminants de la différence de structure par terme de taux d’escompte psychologique caractéristiques des préférences temporelles. Nous avons enfin établi qu’il existe une faible relation entre les paramètres des préférences temporelles, face au risque et sociales.L’ensemble de ces analyses nous ont permis de dériver des conclusions par rapport aux hypothèses de recherche que nous avons formulées et d’interroger la validité de chacune d’elles dans la perspective de déduire les réponses à la problématique de notre recherche. / The discounted utility theory proposed by Samuelson (1937) is one of the dominant paradigms in economics and management especially in finance where it serves as a basis of the Intertemporal Capital Asset Pricing Model (ICAPM) and its version including consumption (ICCAPM). Despite this place, its validity has a framework to explain individuals time preferences has been questioned in recents researches paving the way for amendments and questionings of this framework. Among others, these reseaches introduce the concept of term structure of psychological discount rate. Therefore, a part from exponential discount rate function, we find in the literature seven alternatives discount rate function : Hernstein, proportional, Laibson, Rachlin, Hyperbolic and generalized hyperbolic.Following this work, we initiated a research to provide an answer to the question on the characteristics and driving factors those explain its heterogeneity at an individual level. Thereafter, its relationship with other dimensions of individual preferences (risk and social interaction behavior) are explored. The purpose is to identify among them, the function that is consistent with the observed time preferences, to estimate the underlying parameters and to study the consistency of individual time preference. This research is based on the data collected by experimental study using eighteen time trade-offs, four lottery trade-offs, a dictator game, an ultimatum game and a trust game.Data analysis confirmed previous results on the violation of the time invariant of the psychological value of time hypothesis and established that the studied population is characterized by an heterogeneity with respect to the form of the term structure of psychological discount rate. Individuals are characterized by an Hernstein, Generalized hyperbolic or Laibson psychological discount rate. We found that demographic, social and temporal orientation have a weak link with the individual differences of the term structure of psychological discount rate. Application (a dimension of personality traits) is the most important driving factor of term structure of psychological discount rate forms heterogeneity. We finally established that there is a weak relationship between the parameters of time, risk and social preferences.

L'objectif de cette thèse est d’étudier à côté du risque défaut, le rôle spécifique des risques de volatilité et de co-volatilité dans la formation des taux longs dans la zone euro. On propose en particulier un modèle théorique de choix de portefeuille à deux pays permettant d’évaluer la contribution des primes de risque de volatilité aux processus de contagion et de fuite vers la qualité dans différents épisodes de la crise de la dette souveraine. Ce modèle permet également d’analyser le rôle des achats d’actifs (QE) de la BCE sur l’équilibre des marchés obligataires. Nos tests empiriques suggèrent que les programmes QE de la BCE à partir de mars 2015 n’ont fait qu’accélérer « une défragmentation » des marchés obligataires de la zone euro, apparue plus tôt dans la crise, dès la mise en place de l’OMT. / This thesis examines the specific role of volatility risks and co-volatility in the formation of long-term interest rates in the euro area. In particular, a two-country theoretical portfolio choice model is proposed to evaluate the volatility risk premia and their contribution to the contagion and flight to quality processes. This model also provides an opportunity to analyze the ECB's role of asset purchases (QE) on the equilibrium of bond markets. Our empirical tests suggest that the ECB's QE programs from March 2015 have accelerated the "defragmentation" of the euro zone bond markets.

[pt] Este trabalho propõe um modelo de otimização robusta de pior caso orientado por dados aplicado na seleção de um portfólio de títulos de renda fixa. A gestão das carteiras implica na tomada de decisões financeiras e no gerenciamento do risco através da seleção ótima de ativos com base nos retornos esperados. Como estes são variáveis aleatórias incertas foi incluído um conjunto definido de incertezas estimadas diretamente no processo de otimização, chamados de cenários. Foi usado o modelo de ajuste de curvas Nelson e Siegel para construir as estruturas a termo das taxas de juros empregadas na precificação dos títulos, um ativo livre de risco e alguns ativos com risco de maturidades diferentes. Os títulos prefixados são marcados a mercado porque estão sendo negociados antes do prazo de vencimento. A implementação ocorreu pela simulação computacional usando dados de mercado e dados estimados que alimentaram o modelo.Com a modelagem de otimização robusta foram realizados diferentes testes como: analisar a sensibilidade do modelo frente às variações dos parâmetros verificando seus resultados e a utilização de um horizonte de janela rolante para simular o comportamento ao longo do tempo. Obtidas as composições ótimas das carteiras, foi feito o backtesting para avaliar o comportamento das alocações com o retorno real e também a comparação com o desempenho de umbenchmark. Os resultados dos testes mostraram a adequação do modelo da curva de juros e bons resultados de alocação do portfólio robusto, que apresentaram confiabilidade até em períodos de crise. / [en] This paper proposes a data-driven worst case robust optimization model applied in the selection of a portfolio of fixed income securities. The portfolio management implies in financial decision-making and risk management through the selection of optimal assets based on expected returns. As these are uncertain random variables, was included a defined set of estimated uncertainties directly in the optimization process, called scenarios. The Nelson and Siegel curve fitting model was used to construct the term structure of the interest rates employed in the pricing of securities, a risk-free asset and some risky assets of different maturities. The fixed-rate securities are marked to market because they are being traded before the maturity date. The implementation took place through computational simulation using market data and estimated data that fed the model. With robust optimization modeling were done different tests such as: analyze the sensitivity of the model to the variations of the parameters checking the results and the use of a rolling horizon scheme to simulate behavior over time. Once the optimal portfolio composition was obtained, the backtesting was done to evaluate the behavior of the allocations with the real return and also the comparison with the performance of a benchmark. The results of the tests showed the adequacy of the interest curve model and good allocation results of the robust portfolio, which presented reliability even in times of crisis.

[pt] Tipicamente, a literatura de curva de juros assume que taxas de juros para horizontes longos são compostas por expectativas de taxas de juros curtas que devem vigorar nesse horizonte longo e/ou um prêmio de risco. O objetivo deste trabalho é mostrar evidência de que o peso relativo de um componente expectacional vis-à-vis um componente de prêmio de risco pode depender do tempo e do estado da economia. Ademais, a probabilidade de um Regime da Teoria das Expectativas mostra-se relacionado ao ciclo de negócios. Ainda, os resultados indicam que ao se incorporar a probabilidade destes regimes, é possível intensficar o poder preditivo do diferencial entre os juros longos e o curto tanto para excesso de retornos quanto para atividade econômica. / [en] The yield curve literature typically decomposes long-term interest rates into expected future short-term rates and a risk premium. We show that the relative importance of the expectational component vis-à-vis the risk premium component can be time-varying and state-dependent. Further, the likelihood of an Expectations Hypothesis (EH) State has a clear relation to the business cycle. Moreover, our results indicate that incorporating the probability of these EH states boosts the predictive power of the benchmark yield curve measure, the term spread, both for future excess bond returns and economic activity.

[pt] Esta tese é composta por dois ensaios sobre finanças empíricas. O primeiro se concentra nos mercados de câmbio e apresenta medidas de mudanças na inclinação da estrutura de curto prazo das taxas de juros para os EUA e outros países de G10, usando contratos de futuros de 3 e 6 meses. Essas mudanças na inclinação têm impacto imediato nos retornos da moeda e também forte efeito retardado nas semanas seguintes, o que implica que as moedas são previsíveis tanto dentro quanto fora da amostra. Os investidores que condicionam na inclinação para negociar taticamente uma carteira comprada em moedas G10 contra o Dólar americano melhoram os índices de Sharpe para 0,4-0,9, em relação a 0,15 de uma estratégia de buy and hold. Uma carteira de moeda neutra em dólares que classifica as moedas dos países do G10 de acordo com a inclinação no cross-section também oferece índices de Sharpe mais altos do que outras estratégias de moeda como o carry trade. Essas descobertas são compatíveis com uma reação defasada do mercado de câmbio às informações sobre taxas de juros. O segundo ensaio propõe uma nova medida que usa apenas informações de dispersão cross-section de betas do modelo CAPM para prever retornos agregados de mercado para os EUA. Esta escolha de preditores é baseada em argumentos teóricos simples de que as medidas associadas à dispersão dos betas do CAPM, em alguns cenários, devem ser relacionadas aos retornos futuros de mercado esperados. Essas medidas de dispersão de fato prevêem o prêmio de risco de mercado em vários horizontes e fornecem alto poder preditivo dentro e fora da amostra. O R2 fora da amostra atinge até 10 porcento na frequência anual (0,7 porcento mensal) e são robustos a diferentes janelas de estimação. Ao contrário da maioria das medidas encontradas na literatura, a nossa não é baseado em preço ou valuation ratios. Nossas medidas variam com o ciclo econômico e se correlacionam com outras variáveis de previsão comumente usadas, como razões de dividendo-preço e consumo-riqueza, mas fornecem poder explicativo acima e além dos preditores padrão. Nossos resultados fornecem evidências adicionais de que a dispersão dos betas ao longo do tempo é função da variação temporal do prêmio de risco de mercado. / [en] The thesis is composed of two essays on empirical finance. The first focuses on FX markets and presents measures of interest rates shortterm structure slope changes for the US and other G10 countries using 3- and 6-month futures contracts. These changes in slopes have immediate impact on currency returns but also a strong delayed effect over the following weeks, implying that currencies are predictable both in and outof-sample. Investors that condition on slope to tactically trade a long G10 portfolio improve Sharpe ratios to 0.4-0.9, relative to 0.15 for a buy-andhold strategy. A dollar-neutral currency portfolio that sorts G10 country currencies on the cross-section slope also deliver higher Sharpe ratios than other currency strategies, such as the carry trade. These findings are compatible with delayed currency market reaction to information in interest rates. The second essay proposes a novel measure that solely use crosssectional dispersion information on CAPM betas to forecast aggregate market returns for the US. This choice of predictors is based on simple theoretical arguments that measures associated with the dispersion of CAPM betas, in some settings, should be related with expected future market returns. We find that these dispersion measures do indeed forecast market risk premium over multiple horizons and deliver high in-sample and out-of-sample predictive power: out-of-sample R2 reaches up to 10 percent at the annual frequency (0.7 percent monthly) and are robust to different estimation windows. Unlike most measures in the literature, ours is not a price- or valuation-based ratio. Our approach is also an alternative to models that use the cross-section of valuation ratios to infer the conditional market risk premium. Our measures vary with the business cycle and correlate with other commonly used forecasting variable such as dividend-price or consumption-wealth ratios, but they provide explanatory power above and beyond the standard predictors. Our findings provide additional evidence that the betas dispersion across time is a function of time varying risk premium.

By issuing interest rate derivative contracts, market makers such as large banks are exposed to undesired risk. There are several methods for banks to hedge themselves against this type of risk; one such method is the stochastic programming model developed by Blomvall and Hagenbjörk (2022). The effectiveness of their model relies on accurate pricing of interest rate derivatives and risk factor analysis, both of which are derived from a term structure. Blomvall and Ndengo (2013) present a discretized multiple yield curve framework for term structure measurement that allows for price deviations. The model uses regularization to deal with noise inherent in market price observations, where the regularization counteracts oscillations in the term structure and retains the smoothness of the curve by penalizing the first and second-order derivatives. Consequently, the resulting model creates a trade-off between a smooth curve and market price deviations. Changes in policy rates adjusted by a country’s central bank significantly impact the financial market and its actors. In this thesis, the model developed by Blomvall and Ndengo (2013) was further extended to include these steps in conjunction with monetary policy meetings. Two models were developed to realize the steps in the risk-free curve. The first model introduced an additional deviation term to allow for a shift in the curve. In the second model, the weights in the regularization were adjusted to allow for rapid changes on days surrounding the closest monetary policy meeting. A statistical test was conducted to determine the performance of the two models. The test showed that the model with adjusted regularization outperformed the model with an additional deviation term as well as a benchmark model without steps. However, both step models managed to reduce in-sample pricing errors, while the model with an additional deviation term performed worse than the benchmark model for out-of-sample data, given the current parameter setting. Other parameter combinations would potentially result in different outcomes, but it remains conjectural.

It can be difficult for a sovereign debt manager to see the implications on expected costs and risk of a specific debt management strategy, a simulation model can therefore be a valuable tool. This study investigates how future economic data such as yield curves, foreign exchange rates and CPI can be simulated and how a portfolio optimization model can be used for a sovereign debt office that mainly uses financial derivatives to alter its strategy. The programming language R is used to develop a bespoke software for the Swedish National Debt Office, however, the method that is used can be useful for any debt manager. The model performs well when calculating risk implications of different strategies but debt managers that use this software to find optimal strategies must understand the model's limitations in calculating expected costs. The part of the code that simulates economic data is developed as a separate module and can thus be used for other studies, key parts of the code are available in the appendix of this paper. Foreign currency exposure is the factor that had the largest effect on both expected cost and risk, moreover, the model does not find any cost advantage of issuing inflation-protected debt. The opinions expressed in this thesis are the sole responsibility of the author and should not be interpreted as reflecting the views of the Swedish National Debt Office. / Det kan vara svårt för en statsskuldsförvaltare att se påverkan på förväntade kostnader och risk när en skuldförvaltningsstrategi väljs, en simuleringsmodell kan därför vara ett värdefullt verktyg. Den här studien undersöker hur framtida ekonomiska data som räntekurvor, växelkurser ock KPI kan simuleras och hur en portföljoptimeringsmodell kan användas av ett skuldkontor som främst använder finansiella derivat för att ändra sin strategi. Programmeringsspråket R används för att utveckla en specifik mjukvara åt Riksgälden, men metoden som används kan vara användbar för andra skuldförvaltare. Modellen fungerar väl när den beräknar risk i olika portföljer men skuldförvaltare som använder modellen för att hitta optimala strategier måste förstå modellens begränsningar i att beräkna förväntade kostnader. Delen av koden som simulerar ekonomiska data utvecklas som en separat modul och kan därför användas för andra studier, de viktigaste delarna av koden finns som en bilaga till den här rapporten. Valutaexponering är den faktor som hade störst påverkan på både förväntade kostnader och risk och modellen hittar ingen kostnadsfördel med att ge ut inflationsskyddade lån. Åsikterna som uttrycks i den här uppsatsen är författarens egna ansvar och ska inte tolkas som att de reflekterar Riksgäldens syn.

With the substantial size of the interest rate markets, the importance of accurate pricing, risk measurement and performance attribution can not be understated. However, the models used on the markets often have underlying issues with capturing the market's fundamental behavior. With this thesis, we aim to improve the pricing, risk measurement, and performance attribution of interest rate swap portfolios. The paper is divided into six main parts, by subject, to aid in achieving these goals. To begin with, we validate all cash flows with SEB to increase the validity of the results. Next, we implement an optimization-based model developed by Jörgen Blomvall to estimate multiple yield curves.  By considering innovations of the daily in-sample curves, risk factors are computed with principal component analysis. These risk factors are then used to simulate one-day and ten-day ahead scenarios for the multiple yield curves using a Monte Carlo method. Given these simulated scenarios, risk measures are then computed. When backtested, these risk measurements give an indication on the overall accuracy of the methodology, including the estimated curves, the derived risk factors, and the simulation methodology. Along with the simulation, on each out-of-sample day, monetary performance attribution for the portfolios is also performed. The performance attribution indicates what drives the value change in the portfolio. This can be used in order to evaluate the estimated yield curves and derived risk factors. The risk measurement and performance attribution is done for three different portfolios of interest rate swaps on the EUR, USD, and SEK markets. However, the risk factors are only estimated for EUR data and used for all portfolios.  The main difference to previous work in this area is that, for all implementations, a multiple yield curve environment is studied. Different PCA algorithms are evaluated to increase the precision and speed of the risk factor calculation. Mean reverting risk factors are developed in the simulation framework, along with a Latin hypercube sampling method accounting for dependence in the random variables to reduce variance. We also study the EUR and SEK markets, while the focus in previous literature is on the USD market. Lastly, we calculate and backtest the risk measures value-at-risk and expected shortfall for one-day and ten-day horizons. Four different PCA methods are implemented, a bidiagonal divide and conquer SVD algorithm, a randomized SVD method, an Arnoldi method, and an optimization-based PCA algorithm. We opt to use the first one due to high accuracy and the ability to calculate all eigenpairs. However, we recommend to use the Arnoldi method in future implementations and to further study the optimization-based method. The Latin hypercube sampling with dependence method is able to produce random variables with the same correlation as the input variables. In the simulation, we are able to produce results that pass all backtests for the risk measures considering the USD portfolio. For the EUR and SEK portfolios, it is shown that the risk measures are too conservative. The results of the mean reversion method indicate that it produces slightly less conservative estimates for the ten-day horizon. In the performance attribution, we show that we are able to produce results with small error terms, therefore indicating accurately estimated term structures, risk factors, and pricing. We conclude that we are partly able to fulfill the stated purpose of this thesis due to having produced accurate pricing and satisfactory performance attribution results for all portfolios, and stable risk measures for the USD portfolio. However, it is not possible to state with certainty that improved risk measurements have been achieved for the EUR and SEK portfolios. Although, we present several alternative approaches to remedy this in future implementations.

[pt] Neste estudo, tentamos estimar o impacto da medida intervencionista mais recente e amplamente adotada pelo Banco Central do Brasil no mercado de câmbio sobre a Curva de Cupom Cambial: a emissão de Swaps Cambiais. O objetivo do BCB com essa intervenção era prover o setor privado de proteção contra a volatilidade cambial à época. O trabalho foca no efeito dessas medidas na curva de Cupom Cambial por conta da importância do funcionamento dessa curva para a correta precificação do mercado de dólar futuro, já que, no Brasil, a formação da taxa de câmbio se dá no preço futuro de dólar e não no preço à vista, como é comum nos outros países. Através de Análise de Componentes Principais sobre a Curva de Cupom Cambial, encontramos seus três primeiros componentes (nível, inclinação e curvatura) e os utilizamos para regredi-los em variáveis independentes que representam a série de emissões de Swap por parte do BC. Os resultados indicam que os Swaps Cambiais geram mudanças significativas no nível geral da Curva de Cupom Cambial. Já os Swaps Reversos não apresentam impacto estatisticamente significante no nível, mas sim na inclinação da curva. / [en] In this study, we try to estimate the impact of the most recent currency intervention measure widely adopted by the Central Bank of Brazil and how it affects the Cupom Cambial Curve: the issue of Foreign Exchange Swaps. The BCB s objective with this intervention was to provide the private sector with hedge against exchange rate volatility. This paper focus on the effect of these measures on the Cupom Curve due to the importance of the comprehension of this curve for the correct pricing of the future dollar market, given that, in Brazil, the formation of the foreign exchange rate occurs with the future dollar price and not in the spot price, as is more common in other countries. Through Principal Component Analysis on the Foreign Exchange Coupon Curve, we find its three components (level, slope and curvature) and use it as an explained variable to regress it with independent variables that represent the series of Swap issued by the Central Bank. The results indicate that the Foreign Exchange Swaps generate significant changes in the overall level of the Cupom Cambial Curve. Otherwise, Reverse Swaps don t represent a statistically significant impact on the level but do impact the slope of the curve.