The goal of this thesis is to analyze the mathematical apparatus of the most widespread methods used for the yield curves construction. It aims to introduce not only the various of construction models but also to describe the whole process of creation, while discussing the advantages and disadvantage of individual methods. The first chapter focus on the general theory and the use of the term structure of interest rates in practice. The second part deals with the construction process itself and describes the most frequently used methods. The last chapter then shows the real application of selected methods on given data set and the use of the constructed yield curves for interest rate derivative valuation too.

The interest rate dynamics is an important fundamental for valuation more complex structures of interest rate derivatives. The goal of this diploma thesis is to describe the use of models of interest rate for interest rate option pricing. The paper could be logically divided into two parts, the theoretical one and practical one. In the first part the essentials for pricing theory are introduced as risk neutrality, martingales, stochastic differential calculus, and theory of arbitrage. On their basis four basic yield curve models are derived, Vasicek model, model Cox-Ingersoll-Ross , Black-Derman-Toy and two factor Heath-Jarrow-Morton model. Second part provides the analysis of yields of U.S. Treasury bonds with different maturity. At the end CIR model and BDT binomial tree are used for valuation of option on 10 years yield.

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.

[pt] Risco fiscal afeta a curva de juros no contexto de economias emergentes? Como medir adequadamente esse tipo de risco? Explorando o caso do Brasil, estimamos uma medida alternativa de risco fiscal com base em notícias, utilizando processamento de linguagem de texto. Encontramos que aumento em risco fiscal gera aumento em taxas de juros longas, no prêmio a termo e depreciação na taxa de câmbio. Os efeitos são robustos a uma série de especificações alternativas do índice de risco fiscal, sugerindo que se trata de um fenômeno relevante no cenário brasileiro. / [en] Does fiscal policy risk affect the yield curve in an emerging economy? How can we adequately measure this kind of uncertainty? Exploiting the case of Brazil, we estimate a novel, news-based measure of fiscal policy risk using natural language processing. We show that increases in fiscal policy risk are associated to increases in the levels of long maturities in the yield curve, in the term spread and to a depreciation of the exchange rate. The effects are robust to a series of alternative specifications of the text-based index, suggesting that fiscal risk is a relevant phenomenon in the Brazilian setting.

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.

Purpose: The purpose of this study is to examine how changes in long and short interest rates as well as in the slope of the yield curve affect the stock returns of the four major Swedish banks; Svenska Handelsbanken, Nordea Bank, Swedbank, and Skandinaviska Enskilda Banken. Further, the aim of the research is to compare these findings to how the banks perceive that such changes affect their stock returns. The objective is thereof to detect differences and similarities between regressions and interviews, in order to contribute with insights to how the banks can handle their exposure to interest rate risk. Theoretical Framework: Previous research show that banks’ stock returns are affected by many factors, including cash flow news, interest rates, size of the business, and the macroeconomy as a whole. However, banks’ interest rate margins are set to market rates so these are more exposed to and affected by changes in interest rates, especially short ones, than are non-financial institutions. Furthermore, the low interest rate levels and forecasting errors that have been seen lately have contributed to greater uncertainty and higher risk exposures, making banks’ sensitivity increase. Methodology: A mixture of a qualitative and a quantitative methodology is used, where the former consists of interviewing the banks and the latter of regressions through secondary data from Thomson Reuters Eikon and the Riksbank. Conclusion: The major Swedish banks’ stock returns are generally affected by changes in short interest rates but not by changes in long interest rates, with the exception of Handelsbanken being impervious to all such changes. Swedbank’s stock returns are most sensitive than the other banks’ stock returns and it is the only bank affected by changes in the yield curve slope. However, the banks seem to perceive no crucial difference in how their stock returns are affected by changes in short interest rates and long interest rates, concluding that their perceptions of long interest rates are not as in line with our results as are their perceptions of short interest rates. However, it tends to be a more diffuse relationship between changes in long interest rates and stock returns than between changes in short interest rates and stock returns.

[pt] O Asset Liability Management (ALM) é uma ferramenta essencial para uma administração eficaz de bancos, seguradoras e fundos de pensão, principalmente no que diz respeito ao monitoramento e controle de riscos enfrentados por estas instituições. Dentre estes riscos, o de taxa de juros é uma das principais fontes de perda potencial para uma instituição financeira. Este trabalho tem como objetivo estudar formas de se controlar este tipo de risco. Para tal, será estudada a fundo a estratégia de imunização de carteiras. Esta estratégia consiste em montar uma carteira ótima de forma que a mesma seja imune a variações na taxa de juros, ou seja, independente das variações que ocorram nas taxas de juros, o valor da carteira não se altere. Dois modelos de imunização de carteiras de renda fixa propostos na literatura são estudados detalhadamente. Um utiliza a técnica de análise de componentes principais (ACP), imunizando a carteira na direção destes componentes. O outro modelo usa um método de minimização do risco estocástico. Em ambos, um exemplo ilustrativo é apresentado e uma aplicação prática é feita utilizando-se dados de um fundo de pensão no Brasil (este tipo de estratégia é de extremo interesse para fundos de pensão, que possuem longos fluxos de passivos e que desejam garantir que suas obrigações sejam sempre satisfeitas). Por fim, é feita uma análise dos resultados obtidos após a imunização. / [en] Asset Liability Management (ALM) is an important tool used in the administration of banks, insurance companies and pension funds, especially for monitoring and controlling the risk those institutions usually face. Among the various types of risk, the interest rate risk is one of the main sources of potential loss for a financial institution. This dissertation aims to study ways of controlling this type of risk. Thus, we will thoroughly study the strategy used for Asset Liability Management. This strategy consists in assembling an optimum portfolio in a way that it becomes unaffected by changes in the interest rates. A couple of immunization models for fixed rate portfolios are studied in detail. One of them employs the method of principal component analysis (PCA), immunizing the portfolio in the direction of those components. The other model minimizes the stochastic risk. In both of them, we present an example and use of the method in a Brazilian pension fund (this strategy is highly interesting to pension funds since they work with a long liability cash flow and want to certify their obligations will always be satisfied). Finally, we analyse the results obtained with the two methods.

經濟體的產出缺口一直是政策執行者的觀察重點，當一國出現產出缺口時，代表資源配置並不均衡，將發生通貨膨脹或是失業的現象，如能提早預期到未來是否會出現產出缺口，將可讓政策執行者即早進行政策實施，且有文獻指出，殖利率曲線資料中具有隱含未來經濟狀況之資訊。 本研究以美國財政部與聯準會之公開資料，將以殖利率曲線之斜率進行預測產出缺口；本文研究美國1977年至2016年之國民生產毛額成分與殖利率之資料，目標為建立對於未來一季將出現正向或負向缺口現象之模型，本研究建立三種預測模型進行比較，分別為線性迴歸模型、羅吉斯迴歸模型與機器學習中的支持向量機，以實質GDP的缺口預測而言，研究結果顯示，三者預測準確度均達到65%以上，支持向量機的準確度更達到80.85%。 得出以下結論，第一，殖利率曲線對於未來總體經濟產出缺口具有一定之解釋力；第二，對於高維度之預測模型在機器學習中的支持向量機表現會較一般常用之迴歸模型佳；第三，進出口的預測力在三個模型下均表現較差，可能為殖利率曲線對於進出口並不具有完整有效的資訊，可能有其餘的經濟指標或金融市場資訊可以解釋；第四，對於實質消費與投資等民間部門經濟行為有超過80%的預測力。 / The output gap of the economy has always been the objectives of policy practitioners. When a country appear the output gap, it means that the allocation of resources is not equilibrium and the inflation or unemployment will occur. The output gap will allow policymakers to implement the policy as early as possible, and the literature notes that the information of the yield curve has information about the future economic situation. In this paper, we using the data from the U.S. Department of Treasury and the Federal Reserve to predict the output gap by the slopes of the yield curve. Our goal is to construct the prediction model for the next quarter. To forecast the real GDP gap, three prediction models were compared, linear regression model, logistic regression model and support vector machine. The results show that the accuracy of the three predictions are more than 65%, support vector machine accuracy to reach 80.85%. We can have conclusions showing below: First, the yield curve has significant explanatory power for the overall economic output gap in the future. Second, the support vector machine perform better than the commonly used regression model. Third, the predictive power of real import and export in the three models are poor performance, there may be the rest of the economic indicators or financial market information can be explained. Fourth, the real consumption and investment has the predictive power more than 80% of the forecast.

隨著金融市場的開放，越來越多的金融商品被開發出來以迎合市場參予者的需求，利率衍生性金融商品是一種以利率為標的的一種新金融商品，而這種新金融商品的交易量也是相當的可觀。我們在設計金融商品的第一步就是要去定價，在現實社會中利率是隨機波動的而不是像在B-S的選擇權公式中是固定的。隨機利率模型的用途就是在描述利率隨機波動的行為，進而對利率衍生性金融商品定價。本文嘗試以隨機利率模型估計台灣公債市場的殖利率曲線，而殖利率曲線的建立對於固定收益證券及其衍生性金融商品的定價是很重要的。在台灣大部分的利率模型的研究都是利用模擬的方式做比較，這也許是因為資料取得上的問題，本文利用CKLS(1992)所提出的方式以GMM(Generalized Method of Moment)的估計方法，利用隨機利率模型估計出台灣公債市場的殖利率曲線。本文中將三種隨機利率模型做比較他們分別為: Vasicek model (Vasicek 1977),、隨機均數的Vasicek 模型 (BDFS 1998) ，以及隨機均數與隨機波動度的Vasicek 模型 (Chen,Lin 1996). 後面兩個模型是首次出現在台灣的研究文獻中。在本文的附錄中將提出如何利用偏微分方程式(PDE)的方法求解出這三個模型的零息債券價格的封閉解(Closed-Form Solution)。文中利用台灣商業本票的價格當作零息債券價格的近似值，再以RMSE (Root mean squared Price Prediction Error)作為利率模型配適公債市場價格能力的指標。本文的主要貢獻在於嘗試以隨機利率模型估計出台灣公債市場的殖利率曲線，以及介紹了兩種首次在台灣研究文獻出現的利率模型，並且詳細推導其債券價格的封閉解，這對於想要建構一個新的隨機利率模型的研究人員而言，這是一個相當好的一個練習。 / With the growth in the area of financial engineering, more and more financial products are designed to meet demands of the market participants. Interest rate derivatives are those instruments whose values depend on interest rate changes. These derivatives form a huge market worth several trillions of dollars. The first step to design or develop a new financial product is pricing. In the real world interest rate is not a constant as in the B-S option instead it changes over time. Stochastic interest rate models are used for capturing the volatile behavior of interest rate and valuing interest rate derivatives. Appropriate models are necessary to value these instruments. Here we want to use stochastic interest rate models to construct the yield curve of Taiwan Government Bond (TGB) market. It is important to construct yield curve for pricing some financial instruments such as interest rate derivatives and fixed income securities. 　In Taiwan Although most of the research surrounding interest rate models is intended towards studying their usefulness in valuing and hedging complex interest rate derivatives by simulation. But just a few papers focus on empirical study. Maybe this is due to the problems for data collection. In this paper we want to use stochastic interest models to construct the yield curve of Taiwan’s Government Bond market. The estimation method that we use in this paper is GMM (Generalized Method of Moment) followed CKLS (1992). I introduce three different interest rate model, Vasicek model (Vasicek 1977), Vasicek with stochastic mean model (BDFS 1998) and Vasicek with stochastic mean and stochastic volatility model (Chen,Lin 1996). The last two models first appear in Taiwan’s research. In the Chapter 3, I will introduce these models in detail and in the appendix of my thesis I will show how to use PDE approach to derive each model’s zero coupon bond price close-form solution. In this paper we regard Taiwan CP (cmmercial Paper) rates as a proxy of short rate to estimate the parameters of each model. Finally we use these models to construct the yield curve of Taiwan Government Bonds market and to tell which model has the best fitting bond prices performance. Our metric of performance for these models is RMSE (Root mean squared Price Prediction Error). The main contribution of this study is to construct the yield curve of TGB market and it is useful to price derivatives and fixed income securities and I introduce two stochastic interest rates models, which first appear in Taiwan’s research. I also show how to solve the PDE for a bond price and it is a useful practice for someone who wants to construct his/her own model.

This thesis is composed of three chapters which propose some novel approaches to model and forecast financial time series. The first chapter focuses on high frequency financial returns and proposes a quantile regression approach to model their intraday seasonality and dynamics. The second chapter deals with the problem of forecasting the yield curve including large datasets of macroeconomics information. While the last chapter addresses the issue of modelling the term structure of interest rates. The first chapter investigates the distribution of high frequency financial returns, with special emphasis on the intraday seasonality. Using quantile regression, I show the expansions and shrinks of the probability law through the day for three years of 15 minutes sampled stock returns. Returns are more dispersed and less concentrated around the median at the hours near the opening and closing. I provide intraday value at risk assessments and I show how it adapts to changes of dispersion over the day. The tests performed on the out-of-sample forecasts of the value at risk show that the model is able to provide good risk assessments and to outperform standard Gaussian and Student’s t GARCH models. The second chapter shows that macroeconomic indicators are helpful in forecasting the yield curve. I incorporate a large number of macroeconomic predictors within the Nelson and Siegel (1987) model for the yield curve, which can be cast in a common factor model representation. Rather than including macroeconomic variables as additional factors, I use them to extract the Nelson and Siegel factors. Estimation is performed by EM algorithm and Kalman filter using a data set composed by 17 yields and 118 macro variables. Results show that incorporating large macroeconomic information improves the accuracy of out-of-sample yield forecasts at medium and long horizons. The third chapter statistically tests whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities. Still, central banks and public wealth managers rely heavily on it. Using a non-parametric resampling technique and zero-coupon yield curve data from the US market, I find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson and Siegel model, at a 95 percent confidence level. I therefore conclude that the Nelson and Siegel yield curve model is compatible with arbitrage-freeness.