O presente trabalho testa uma alternativa de ajuste da estrutura a termo da taxa de juros brasileira bem como a sua previsão através de uma variação do modelo Diebold e Li (2006) focando principalmente em seu fator de decaimento exponencial. Esta variação do fator de decaimento ocorre distintamente em dois momentos do trabalho, primeiramente no ajuste da curva e após quando da previsão desta. No ajuste, o encontro deste parâmetro é feito através de ferramenta computacional, buscando o fator de decaimento que reduz a diferença de mínimos quadrados em relação aos pontos originais capturados no mercado de juros futuro brasileiro em conjunto dos três outros fatores do modelo. A previsão da estrutura a termo utiliza modelos auto regressivos para estimar as próximas curvas no horizonte de um período. A importância deste estudo reside em conhecer a aderência do modelo proposto à curva de juros brasileira testando sua eficiência quando utilizados os pressupostos enunciados. / This study tests an alternative adjustment of the term structure of Brazilian interest rate and its prediction through a variation of the Diebold and Li (2006) model focusing mainly on his exponential decay factor. The variation of the decay factor occurs in two distinct moments of this work, in the curve fitting and after this in the forecasting. During the setting, this parameter is mesured through computational tool, seeking the decay factor that reduces the difference in least squares relative to the original points captured in the Brazilian market future interest together the other three factors of the model. To Forecast the term structure is used auto regressive models to estimate the upcoming curves. The importance of this study lies in knowing the adherence of the proposed to the Brazilian yield curve testing its efficiency when utilized the assumptions listed in the model.

Este trabalho testa a validade da Hipótese das Expectativas, segundo a qual as taxas de juros de longo prazo são formadas pela média das expectativas sobre as taxas de curto prazo futuras. O estudo baseia-se em dois artigos reconhecidos internacionalmente: Fama e Bliss (1987) e Cochrane e Piazzesi (2005). Os testes são realizados utilizando-se retornos em excesso e taxas forward mensais para títulos com prazo de vencimento entre dois e cinco anos. A base de dados consiste em observações mensais da taxa à vista de contratos futuros de DI. Os resultados apontam para a rejeição da HE para o caso brasileiro. Uma combinação linear de taxas forward é capaz de explicar a variação dos retornos em excesso com R² de até 0,63 para um título com maturidade em dois anos. / This work tests the validity of Expectations Hypothesis (EH), which posts that the long-term rates are an average of future expectations of short-term rates. The study is based on two internationally recognized papers: Fama e Bliss (1987) and Cochrane e Piazzesi (2005). The tests are performed using monthly observations on excess returns and forward rates for 2 to 5 year bonds. The data consists in monthly observations of ID future contracts yields. The results suggest rejection the EH for the Brazilian case. A linear combination of forward rates is able to explain excess returns variation with R² up to 0.63 for 2-year bonds.

Este trabalho testa a validade da Hipótese das Expectativas, segundo a qual as taxas de juros de longo prazo são formadas pela média das expectativas sobre as taxas de curto prazo futuras. O estudo baseia-se em dois artigos reconhecidos internacionalmente: Fama e Bliss (1987) e Cochrane e Piazzesi (2005). Os testes são realizados utilizando-se retornos em excesso e taxas forward mensais para títulos com prazo de vencimento entre dois e cinco anos. A base de dados consiste em observações mensais da taxa à vista de contratos futuros de DI. Os resultados apontam para a rejeição da HE para o caso brasileiro. Uma combinação linear de taxas forward é capaz de explicar a variação dos retornos em excesso com R² de até 0,63 para um título com maturidade em dois anos. / This work tests the validity of Expectations Hypothesis (EH), which posts that the long-term rates are an average of future expectations of short-term rates. The study is based on two internationally recognized papers: Fama e Bliss (1987) and Cochrane e Piazzesi (2005). The tests are performed using monthly observations on excess returns and forward rates for 2 to 5 year bonds. The data consists in monthly observations of ID future contracts yields. The results suggest rejection the EH for the Brazilian case. A linear combination of forward rates is able to explain excess returns variation with R² up to 0.63 for 2-year bonds.

Neste trabalho, estudam-se métodos que consideram a natureza funcional da Estrutura a Termo da Taxa de Juros (ETTJ) para fazer previsões fora da amostra. São estimados modelos não-paramétricos para dados funcionais (NP-FDA) e séries temporais funcionais (FTS). O primeiro se baseia em um estimador de regressão proposto por Ferraty e Vieu (2006), que utiliza funções Kernel para atribuir pesos localmente às variáveis funcionais. Já o segundo se baseia no trabalho de Hays, Shen e Huang (2012), que estimam a ETTJ através de um modelo de fatores dinâmicos, que por sua vez são estimados através de análise de componentes principais funcional. Testa-se a capacidade de previsão dos modelos com a ETTJ americana, para os horizontes de 1, 3, 6 e 12 meses, e comparam-se os resultados com modelos benchmark, como Diebold e Li (2006) e o passeio aleatório. Principal foco deste trabalho, as estimações com métodos NP-FDA não tiveram resultado muito bons, obtendo sucesso apenas com maturidades e horizontes muito curtos. Já as estimações com FTS tiveram, no geral, desempenho melhor que os métodos escolhidos como benchmark. / This work studies methods that takes the Yield Curve's functional nature into account to produce out-of-sample forecasts. These methods are based in nonparametric functional data analysis (NP-FDA) and functional time series (FTS). The former are based in a functional regressor estimator proposed by Ferraty e Vieu (2006) that includes Kernel functions to do local weighting between the functional variables. The latter are based on the paper by Hays, Shen and Huang (2012), that forecasts the Yield Curve based in a dynamic factors model, in which the factors are determined by functional principal component analysis. Their forecasting capability is tested for the american's Yield Curve database for 1, 3, 6 and 12 months. The results from the functional methods models are then compared to benchmarks widely used in the literature, such as the random walk and the Diebold and Li (2006). Main focus on this work, the NP-FDA methods didn't produce very good forecasts, being successful only for very low maturities and short forecast horizons. The forecasts generated by the FTS methods were, in general, better than our chosen benchmarks.

O presente trabalho testa uma alternativa de ajuste da estrutura a termo da taxa de juros brasileira bem como a sua previsão através de uma variação do modelo Diebold e Li (2006) focando principalmente em seu fator de decaimento exponencial. Esta variação do fator de decaimento ocorre distintamente em dois momentos do trabalho, primeiramente no ajuste da curva e após quando da previsão desta. No ajuste, o encontro deste parâmetro é feito através de ferramenta computacional, buscando o fator de decaimento que reduz a diferença de mínimos quadrados em relação aos pontos originais capturados no mercado de juros futuro brasileiro em conjunto dos três outros fatores do modelo. A previsão da estrutura a termo utiliza modelos auto regressivos para estimar as próximas curvas no horizonte de um período. A importância deste estudo reside em conhecer a aderência do modelo proposto à curva de juros brasileira testando sua eficiência quando utilizados os pressupostos enunciados. / This study tests an alternative adjustment of the term structure of Brazilian interest rate and its prediction through a variation of the Diebold and Li (2006) model focusing mainly on his exponential decay factor. The variation of the decay factor occurs in two distinct moments of this work, in the curve fitting and after this in the forecasting. During the setting, this parameter is mesured through computational tool, seeking the decay factor that reduces the difference in least squares relative to the original points captured in the Brazilian market future interest together the other three factors of the model. To Forecast the term structure is used auto regressive models to estimate the upcoming curves. The importance of this study lies in knowing the adherence of the proposed to the Brazilian yield curve testing its efficiency when utilized the assumptions listed in the model.

The thesis analyzed the impacts of fiscal developments on the yield curve using quarterly data on the Czech economy over the period 2000:1 -- 2012:4. This thesis thoroughly reviewed the previous theoretical and empirical literature in order to sort out the rather inconclusive results of previous studies according to their main findings and implemented methodology. The empirical part consists of the estimation of the effects of budget deficits and government debt on the spread between the three-month and five-year interest rates, which closely reflects the effects of fiscal policy on the yield curve. The reduced-form equation was estimated by OLS. Since the estimated coefficients were not statistically significantly different from zero, this thesis did not confirm the conventional macroeconomic view of positive impacts on yields.

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

Predicting U.S. recessions using the slope of the Treasury yield curve has been the focus of extensive research over the past two decades. This yield curve has consistently predicted economic downturns in the United States whenever the curve becomes flat or inverted and recent research has concluded that adding the federal funds rate produces a more accurate model. With the recent recession of 2008 and the housing market's suspected role, I use new data and add a housing index variable to previous models in order to test the correlation and improve the predictive power of the overall model. I run multiple probit regressions to estimate probabilities of a recession within a number of future quarters. I find that models that include the housing index variable in addition to the yield curve and federal funds rate variables give a better in-sample fit and performance than models that do not use it. I discuss the implication of these results in light of the recent recession, and in terms of what this could imply for the future.

Interest rates and foreign exchange spots are widely used within financial products. It is important to understand the risk arising from products that depend on interest rates and/or foreign exchange spots. In this project, the Hull-white model, a non-parametric and a semi-parametric bootstrap will be investigated for simulations of the interest rate of USD, EUR and SEK in conjunction with its corresponding foreign exchange spot. Models were first studied for dollar interest rates and the best model was selected by using variance/autocovariance tests and quantile tests. The chosen model was then used in the simulation of the interest rate in conjunction with the foreign exchange spots. The result from the tests demonstrated that the non-parametric bootstrap model performed the best and was used to simulate the interest rate in conjunction with the foreign exchange spots. The multiple simulations were used to back test a synthetic portfolio using a quantile test. The simulated distribution was found to be acceptable which therefore simulates an acceptable risk. We used data up until 2015 for the tests, this for not including the federal reserve raising the interest rate in the later part of 2015. Avoiding changes in the Fed funds rate was necessary as they are not predictable from sampling from historical data as is done in the model but they do have a very large impact on the shorter end of the curve. The findings in this project suggests that the non-parametric bootstrap model could be used in multiple curve simulations, which could be used for calculations of potential future risk for financial products. This is very important for companies involved with financial products, since strict rules and regulations have to be followed regarding risks within these products.

This thesis is a comparative study where the question is whether a neural network approach can outperform the principal component analysis (PCA) approach for predicting changes of interest rate curves. Today PCA is the industry standard model for predicting interest rate curves. Specifically the goal is to better understand the correlation structure between Swedish and European swap rates. The disadvantage with the PCA approach is that only the information contained in the covariance matrix can be used and not for example whether or not the curve might behave different depending on the current state. In other words, some information that might be quite important to the curve dynamic is lost in the PCA approach. This raises the question whether the lost information is important for prediction accuracy or not. As previously been shown by Alexei Kondratyev in the paper "Learning Curve Dynamics with Artificial Neural Networks", the neural network approach is able to use more information in the data and therefore has potential to outperform the PCA approach. Our thesis shows that the neural network approach is able to achieve the same or higher accuracy than PCA when performing long term predictions. The results show that the neural network model has potential to replace the PCA model, however, it is a more time consuming model. Higher accuracy can probably be achieved if the network is more optimized. / Det här är en jämförande studie där syftet är att undersöka hurvida noggrannare prediktioner kan uppnås genom att använda sig av artificiella neurala nätverk (ANN) istället för principalkomponentanalys (PCA) för att förutspå swapräntekurvor. PCA är idag industristandard för att förutspå räntekurvor. Specifikt är målet att bättre kunna förstå korrelationsstrukturen mellan de Svenska swapräntorna och de Europiska swapräntorna. En nackdel med PCA är att den enda tillgängliga informationen sparas i kovariansmatrisen. Det kan till exempel vara fallet att kurvan beter sig väldigt annorlunda beroende på om de nuvarande räntenivåerna är höga eller låga. Eftersom att sådan information går förlorad i PCA-modellen ligger intresset i att undersöka hur mycket noggrannare prediktionerna kan bli om man tar tillvara på ännu mer av informationen i datan. Som Alexei Kondratyev visar i rapporten "Learning Curve Dynamics with Artificial Neural Networks", så har ANN-modellen potential att ersätta PCA-modellen för att förutspå räntekurvor. I denna studie framgår det att ANN-modellen uppnår samma eller bättre resultat jämfört med PCA-modellen vid längre prediktioner.