Since arbitrage-free is a desirable theoretical feature in a healthy financial market, many efforts have been made to construct arbitrage-free models for yield curves. However, little attention is paid to review if such restriction will improve yield forecast. We evaluate the importance of arbitrage-free restriction on dynamic Nelson-Siegel term structure when forecasting yield curves. We find that it doesn’t help. We also compare these two Nelson-Siegel dynamic models with a benchmark dynamic model and show that Nelson-Siegel structure improve forecasts for long-maturity yields. / text

Neste trabalho, tínhamos por objetivo propor um modelo dinâmico de estrutura a termo de taxas de juros com variáveis macroeconômicas baseado na formulações de Diebold e Li (2006) e Nelson e Siegel (1987) (DNS). A estrutura de estimação proposta permite utilizar dados de frequências distintas, combinando observações diárias de curvas de juros e mensais de variáveis macroeconômicas de interesse através de uma estrutura MIDAS - Mixed Data Sampling. Também utilizamos uma estrutura de volatilidade estocástica multivariada para os fatores latentes e variáveis macroeconômicas e também permitimos que o parâmetro de decaimento do modelo DNS varie no tempo, permitindo capturar mudanças na estrutura de volatilidade condicional e no formato das curvas em períodos longos. O procedimento de estimação é baseado em métodos Bayesianos usando Markov Chain Monte Carlo. Aplicamos este modelos para a curva de juros de títulos do Tesouro Americano entre 1997 e 2011. Os resultados indicam que incorporação de informações diárias e mensais em um mesmo modelo permite ganhos significantes de ajuste, superando as estimativas usuais baseadas em modelos sem informações macroeconômicas e nos métodos usuais de estimação do modelo de Diebold e Li (2006) / In this present work, we propose a dynamic model for the term structure of interest rates with macroeconomic variables based on Diebold e Li (2006)\'s and Nelson e Siegel (1987)\'s researches. The estimation procedure we intend to build allows time series data sampled at different frequencies, mixing daily observations of yield curves and monthly observations of macroeconomic variable through a Mixed Data Sampling (MIDAS) regression. We also make use of a multivariate stochastic volatility structure for the latent factors and allow the parameter that governs the exponential decay rate to vary trough time, which enables us to capture changes both in the conditional volatility structure and in the curve\'s shapes during long periods. The estimation procedure is based on Baeysian inference trough the usage of of Markov Chain Monte Carlo (MCMC) method. We applied these models to the U.S. Treasure bonds\' yield curve from 1997 to 2011. The results denote that joining daily and monthly information into the same model allows significant gains on fitting these models to the term structure, overcoming the usual estimates based on models without macroeconomics information and on regular estimation methods of Diebold e Li (2006)\'s model.

Neste trabalho, tínhamos por objetivo propor um modelo dinâmico de estrutura a termo de taxas de juros com variáveis macroeconômicas baseado na formulações de Diebold e Li (2006) e Nelson e Siegel (1987) (DNS). A estrutura de estimação proposta permite utilizar dados de frequências distintas, combinando observações diárias de curvas de juros e mensais de variáveis macroeconômicas de interesse através de uma estrutura MIDAS - Mixed Data Sampling. Também utilizamos uma estrutura de volatilidade estocástica multivariada para os fatores latentes e variáveis macroeconômicas e também permitimos que o parâmetro de decaimento do modelo DNS varie no tempo, permitindo capturar mudanças na estrutura de volatilidade condicional e no formato das curvas em períodos longos. O procedimento de estimação é baseado em métodos Bayesianos usando Markov Chain Monte Carlo. Aplicamos este modelos para a curva de juros de títulos do Tesouro Americano entre 1997 e 2011. Os resultados indicam que incorporação de informações diárias e mensais em um mesmo modelo permite ganhos significantes de ajuste, superando as estimativas usuais baseadas em modelos sem informações macroeconômicas e nos métodos usuais de estimação do modelo de Diebold e Li (2006) / In this present work, we propose a dynamic model for the term structure of interest rates with macroeconomic variables based on Diebold e Li (2006)\'s and Nelson e Siegel (1987)\'s researches. The estimation procedure we intend to build allows time series data sampled at different frequencies, mixing daily observations of yield curves and monthly observations of macroeconomic variable through a Mixed Data Sampling (MIDAS) regression. We also make use of a multivariate stochastic volatility structure for the latent factors and allow the parameter that governs the exponential decay rate to vary trough time, which enables us to capture changes both in the conditional volatility structure and in the curve\'s shapes during long periods. The estimation procedure is based on Baeysian inference trough the usage of of Markov Chain Monte Carlo (MCMC) method. We applied these models to the U.S. Treasure bonds\' yield curve from 1997 to 2011. The results denote that joining daily and monthly information into the same model allows significant gains on fitting these models to the term structure, overcoming the usual estimates based on models without macroeconomics information and on regular estimation methods of Diebold e Li (2006)\'s model.

It always exists different methods/models to build a yield curve from a set of observed market rates even when the curve completely reproduces the price of the given instruments. To create an accurate and smooth interest rate curve has been a challenging all the time. The purpose of this thesis is to use the real market data to construct the yield curves by the bootstrapping method and the Smith Wilson model in order to observe and compare the performance ability between the models. Furthermore, the extended Nelson Siegel model is introduced without implementation. Instead of implementation I compare the ENS model and the traditional bootstrapping method from a more theoretical perspective in order to perceive the performance capabilities of them.

For a long time, being able to model and mitigate financial risk has been a key success factor for institutions. Apart from an internal incentive, legal and regulatory requirements continue to develop which increases the need for extensive internal risk control. Interest rate risk in the banking book ("IRRBB") alludes to the cur- rent or prospective risk to the bank’s earnings and capital emerging from adverse movements in interest rates that influence the bank’s banking book positions. When interest rates change, the value but also the timing of future cash flows are affected. Thus, the underlying value of a bank’s liabilities and assets and other off-balance sheet items change as a consequence, and therefore its economic value. In 2004, the Basel Committee on Banking Supervision published a paper Principles for the Management and Supervision of Interest Rate Risk which later lead the European Banking Authority ("EBA") to publish a renewed framework in 2016. In December 2021, the EBA published a draft of an updated version of this framework. This paper investigates how banks and risk managers should model IRRBB under these new guidelines. This is achieved by constructing an IRRBB model which is then evaluated to see whether the IRRBB framework provided by the EBA is adequate and comprehensive. The IRRBB model by the EBA is fundamentally constructed by creating six different shock scenarios where the yield curve is stressed (parallel- , short rate-, and long rate shifts). Thereafter, one measures risk by investigating how these shifts affect the bank’s or financial institutions’ economic value and net interest income. In this paper, additional stressed scenarios were produced through Principal Component Analysis and Monte Carlo Simulations. This paper found that the framework by the EBA is adequate and formulates good methods. However, the framework is not fully standardized and comprehensive, and some computations and methods are left for the institution to decide. This is most likely due to the uniqueness of each institution and that it is hard to formulate methods that are pertinent for all. A more complete, standardized framework would however be advantageous for, on the one hand, governing agencies which would benefit from decreasing the number of resources needed when supervising institutions’ internal models. On the other, institutions would benefit from decreasing the probability of potentially overlooking some risk. Furthermore, this would help companies de- crease their capital requirement, which is desirable. / Att modellera och minska finansiella risker har under lång tid varit en nyckelfaktor för företags framgång. Förutom interna incitament fortsätter regulatoriska krav att utvecklas vilket ökar behovet av omfattande intern riskkontroll. Ränterisk i bankbo- ken ("IRRBB") anspelar på den nuvarande eller framtida risken till bankens intäkter och kapital som kommer från ogynnsamma rörelser i räntor som påverka bankens positioner i bankboken. När räntorna förändras påverkas värdet men också tid- punkten för framtida kassaflöden. Således förändras det underliggande värdet av en banks skulder och tillgångar och andra poster utanför balansräkningen som en konsekvens, och därmed dess ekonomiska värde. 2004 publicerade Basel Commit- tee on Banking Supervision ("BCBS") ett dokument Principles for Management and Supervision of Interest Rate Risk som senare ledde till att European Banking Authority ("EBA") publicerade ett förnyat ramverk 2016. I december 2021 publicerade EBA ett utkast till en uppdaterad version av detta ramverk. Denna rapport undersöker hur banker och riskhanterare bör modellera IRRBB i enlighet med dessa nya riktlinjer. Detta uppnås genom att konstruera en IRRBB-modell som sedan utvärderas för att se om det IRRBB-ramverk som tillhandahålls av EBA är adekvat och heltäckande. IRRBB-modellen av EBA är i grunden konstruerad genom att skapa sex olika chockscenarier där avkastningskurvan är stressad (parallell-, kort- och långränteskiften). Därefter mäts risk genom att undersöka hur dessa förskjutningar påverkar bankens eller finansiella institutioners ekonomiska värde och ränteinkomstnetto. I detta dokument har ytterligare stressade scenarier tagits fram genom Principalkomponentanalys och Monte Carlo Simuleringar. Detta dokument fann att EBA:s ramverk är adekvat och formulerar bra metoder. Ramverket är dock inte helt standardiserat och heltäckande och vissa beräkningar och metoder lämnas åt företagen att bestämma. Detta beror med största sannolikhet på varje institutions unika karaktär och att det är svårt att formulera metoder som är relevanta för alla. Ett mer komplett, standardiserat ramverk skulle dock vara fördelaktigt för å ena sidan styrande myndigheter som skulle gynnas av att minska mängden resurser som behövs när de övervakar institutionernas interna modeller. Å andra sidan skulle företag dra fördel av att att minska sannolikheten för att eventuellt förbise vissa risker. Dessutom skulle detta hjälpa företag att minska sitt kapitalkrav, vilket är önskvärt.

無 / Existing literature has shown that force of mortality has amazing resemblance of interest rate. It is then tempting to extend existing model of interest rate model context to mortality modeling. We apply the model in Diebold and Li (2006) and other models that belong to family of yield rate model originally proposed by Nelson and Siegel (1987) to forecast (force of) mortality term structure. The fitting performance of extended Nelson-Siegel model is comparable to the benchmark Lee-Carter model. While forecasting performance is no better than Lee-Carter model in younger ages, it is at the same level in elder ages. The forecasting performance increases for 5-year ahead forecast is better than 1-year ahead comparing to Lee-Carter forecast. In the end, the forecast outperforms Lee-Carter model when age dimension is trimmed to age 20-100.

Usar ativos financeiros para extrair as expectativas de mercado para algumas variáveis macroeconômicas é uma prática comum na literatura de Macro-Finanças. Nessa dissertação utilizamos títulos brasileiros para extrairmos as expectativas tanto do câmbio quanto da inflação com o uso de fatores latentes do tipo Nelson-Siegel. No primeiro capítulo desenvolvemos um modelo que tenta incorporar expectativas do mercado financeiro com os fundamentos macroeconômicos dessa variável. O modelo desenvolvido aqui difere dos modelos anteriores ao permitir volatilidades condicionais que parecem ser muito importantes no mercado cambial. Os resultados encontrados aqui indicam que os modelos com os fatores latentes e as variáveis macroeconômicas tem um poder de previsão melhor do que os modelos puramente macroeconômicos. Além disso, parece haver uma relação entre as variáveis macroeconômicas e a curva de diferencial de juros entre os países. Já no segundo capítulo utilizamos o diferencial entre rendimentos dos títulos reais e nominais usadas como preditores da inflação. O modelo aqui apresentado faz uma decomposição desse diferencial de juros, em prêmios de risco e inflação implícita usando um modelo paramétrico baseado em condições de não-arbitragem. As estimações da de inflação implícita do modelo se mostram estimadores não viesados da inflação futura para horizontes mais curtos e carregam informação para horizontes mais longos. Além disso, mostram resultados superiores que o uso somente do diferencial / Use financial assets to extract market expectations for some macroeconomic variables is a common practice in Macro-Finance literature. In this dissertation we use Brazilian securities to extract the expectations of both the exchange rate as inflation using Nelson- Siegel factors. In the first chapter we developed a model that incorporates these financial market expectations with macroeconomic variables, which are the foundations of this variable. The model developed here differs from previous models by allowing conditional volatilities that seem to be very important in the foreign exchange market. The study findings indicate that the models with latent factors and macroeconomic variables has better preditive power than purely macroeconomic models. In addition,indicates that there is a relationship between macroeconomic variables and the interest rate differential curve between countries. In the second chapter we use the spread between real and nominal bonds used as predictors of inflation. The model presented here is a decomposition of this interest differential in risk premiums and implied inflation using a parametric model based on no-arbitrage conditions. Estimates of implied inflation are non biased estimators of future inflation for shorter horizons and carry information over longer horizons. In addition, the implied inflation has superior results than that only using the differential

This thesis investigates the use of realized volatility features from high frequency data in com- bination with neural networks to improve forecasts of the yield curve of government bonds. I use high frequency data on futures of four U.S. Treasury securities to estimate the Nelson-Siegel yield curve and realized variance of its parameters over the period of 25 years. The estimated parameters are used in prediction of the level, slope and curvature of the yield curve using an LSTM neural network and compared to the Dynamic Nelson-Siegel model. Results show that the use of realized variance and neural network outperforms autoregressive methods in prediction of the level and curvature in daily and monthly forecasts. The yield curve of government bonds itself has a predictive power on multiple macroeconomic variables, therefore improvements in its forecastability may have broader implications on forecasting the overall state of the economy.

Usar ativos financeiros para extrair as expectativas de mercado para algumas variáveis macroeconômicas é uma prática comum na literatura de Macro-Finanças. Nessa dissertação utilizamos títulos brasileiros para extrairmos as expectativas tanto do câmbio quanto da inflação com o uso de fatores latentes do tipo Nelson-Siegel. No primeiro capítulo desenvolvemos um modelo que tenta incorporar expectativas do mercado financeiro com os fundamentos macroeconômicos dessa variável. O modelo desenvolvido aqui difere dos modelos anteriores ao permitir volatilidades condicionais que parecem ser muito importantes no mercado cambial. Os resultados encontrados aqui indicam que os modelos com os fatores latentes e as variáveis macroeconômicas tem um poder de previsão melhor do que os modelos puramente macroeconômicos. Além disso, parece haver uma relação entre as variáveis macroeconômicas e a curva de diferencial de juros entre os países. Já no segundo capítulo utilizamos o diferencial entre rendimentos dos títulos reais e nominais usadas como preditores da inflação. O modelo aqui apresentado faz uma decomposição desse diferencial de juros, em prêmios de risco e inflação implícita usando um modelo paramétrico baseado em condições de não-arbitragem. As estimações da de inflação implícita do modelo se mostram estimadores não viesados da inflação futura para horizontes mais curtos e carregam informação para horizontes mais longos. Além disso, mostram resultados superiores que o uso somente do diferencial / Use financial assets to extract market expectations for some macroeconomic variables is a common practice in Macro-Finance literature. In this dissertation we use Brazilian securities to extract the expectations of both the exchange rate as inflation using Nelson- Siegel factors. In the first chapter we developed a model that incorporates these financial market expectations with macroeconomic variables, which are the foundations of this variable. The model developed here differs from previous models by allowing conditional volatilities that seem to be very important in the foreign exchange market. The study findings indicate that the models with latent factors and macroeconomic variables has better preditive power than purely macroeconomic models. In addition,indicates that there is a relationship between macroeconomic variables and the interest rate differential curve between countries. In the second chapter we use the spread between real and nominal bonds used as predictors of inflation. The model presented here is a decomposition of this interest differential in risk premiums and implied inflation using a parametric model based on no-arbitrage conditions. Estimates of implied inflation are non biased estimators of future inflation for shorter horizons and carry information over longer horizons. In addition, the implied inflation has superior results than that only using the differential

In practice, yield curves, i.e. plots of relation between yields and times to maturity for a group of comparable securities, are an important tool for assets and liabilities pricing as well as for financial decision making. The theoretical risk-free yield curve represents the term structure of interest rates that are used e.g. in insurance industry for pricing the liabilities, for which reserves are created, or also as a benchmark for pricing other assets in the market. When constructing the yield curve, it is not possible to observe yields of a group of assets for all maturities. That is why we use various mathematical methods which enable us to construct the yield curve also for unobserved maturities. In this thesis, some of these methods are introduced. The Svensson's method is one of the most important and frequently used ones. We use this method to derive the coupon curve from Czech government bonds aiming to construct the risk-free zero coupon yield curve. Later on, we use different weights for particular bonds trying to improve pricing of all the bonds based on the derived curve. Then, we also look for the curve that minimizes the mean squared error of estimated (compared to observed) prices. Because problems with liquidity can appear especially for long maturities, we apply all of the procedures to a...