Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

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Models of the term structure of interest rates play a central role in the modern theory of pricing bonds and other interest rate claims. Term structure models based on the principle of no-arbitrage, especially those of the Heath-Jarrow-Morton (1992) class, have become very popular recently, both with academics and practitioners. Surprisingly however, although the implied volatility function plays a crucial role in these no-arbitrage term structure models, there is little systematic evidence to guide optimal model specification within this broad class. We study the implied volatility in the Heath-Jarrow-Morton framework using Eurodollar futures options data. We estimate a daily time series of forward rates within the HJM framework such that, by construction, the predicted futures prices from our model exactly match the observed futures prices. Next, we estimate a daily time series of volatility parameters such that the sum of squared errors between futures options prices predicted by the model and observed futures options prices is minimized. We use the six different volatility specifications suggested by Amin and Morton (1994) within the HJM class of models to price interest rate claims. Since the volatilities are the only unobservables, we use these models to infer the volatilities from the market prices of Eurodollar futures options over the 1987-1998 periods. The minimized sum of squared errors in the option prices is used as the measure of accuracy of each specific model. Each model differs from the others in its ability to match the market option prices and the time required for the computation. We compare the performances of the six volatility specifications in the accuracy-versus-computation time tradeoff. We document the systematic biases between the model and market prices as a function of option type, maturity, and moneyness. We also examine alternative numerical implementations of HJM models using the six volatility specifications. In particular, we analyze the impact on accuracy and computation time of using different numbers of time-steps. We also examine the effect of using time-steps of varying lengths within the same estimation procedure, and of ordering the time-steps in different ways. / Ph. D.

No / This article develops a novel approach for measuring market expectations and term premia in the term structure of interest rates. Key components of this approach are generic impact measures of state variables in a Gaussian dynamic term structure model. These measures are inherent in a particular state variable regardless of how other state variables are defined within the model. With the help of these measures, the approach gives rise to market expectations that predict yield changes well, and term premia with a legitimate impact on the forward curve. In my empirical analysis, I show the generic impact of the short rate on the yield curve, and present observations of the historical dynamics of market expectations and term premia. The calibrated model is also employed to study the impacts of recent unconventional monetary policies.

M.Com. (Financial Economics) / The use of the yield curve spread in forecasting future recessions has become popular as it is a simple tool to use, due to the positive relationship between the yield curve spread and economic activity. The inversion or flattening of the yield curve spread usually signals a future recession. This has been the subject of several studies both internationally and in South Africa. This research provides an analysis of the yield curve spread’s ability to accurately forecast future recessions in South Africa through the use of three probit models. Furthermore, the yield curve spread’s ability to estimate is compared to that of share prices, using the JSE All Share Index. This research extends on studies by Khomo and Aziakpono (2006) and Clay and Keeton (2011), who used the static and dynamic probit models to forecast recessions in South Africa. In addition to these models, this research also makes use of the business cycle conditionally independent probit model for estimation. The findings suggest that share prices improve the yield curve spread’s ability to forecast recessions when estimating using the static probit model; however when comparing the results between the financial variables, the yield curve spread continues to produce the best forecast of recessions in South Africa. These results support those of Khomo and Aziakpono (2006) and Clay and Keeton (2011). Of the three probit models, the dynamic probit model estimate using the yield curve spread produced the most accurate forecast of recessions one quarter ahead. Therefore, the yield curve spread continues to provide the most accurate forecast of recessions in South Africa.

This dissertation treats two different themes. The first, addressed in Chapter 1, regards the pricing of interest rate swaps. The second, studied in the remaining two chapters, regards the implications of monetary policy for the term structure of interest rates.The pricing of interest rate swaps An interest rate swap is an agreement between two parties to exchange fix for floating interest rate payments for a certain period of time. Floating rate payments are made at a floating-rate index, e.g. the three-month interbank rate, while the fixed rate payment, the swap rate, is determined on the market. The swap rate may include a compensation for credit risk depending on the counterparty's credit quality, but in the standard agreement there is no exchange of principal, only interest is transacted, and this effectively reduces concerns about credit risk. The swap spread for a given maturity is the difference between the swap rate and the risk-free rate, measured as the yield on a government bond with similar cash flows. If the standard swap agreement entails negligible credit risk one might expect swap spreads to be low and stable, but market swap spreads vary over time. There are periods when swap spreads are low in accordance with the general theory, but there are also periods when swap spreads reach levels that seem high.The first chapter of this dissertation examines a setting where a positive swap spread arises as part of an equilibrium in a perfectly competitive capital market. The model is one of insurance under adverse selection. A firm that seeks debt financing can insure itself against interest rate risk either by borrowing long-term or by borrowing short-term and entering a pay fix - receive float interest rate swap. The latter alternative allows for a partial hedge as the firm can choose to swap only a fraction of the nominal amount. In this setting, if firms' credit quality and interest rate risk tolerance are correlated creditors can use the pricing of interest rate swaps as a screening device. A low-risk firm, being a firm with favorable private information, selects short-term borrowing and partial insurance. A high-risk firm, being a firm with less favorable prospects, is by assumption also less risk tolerant. It therefore has a higher demand for insurance and the equilibrium swap spread is set such that the high-risk firm finds it more beneficial to borrow long-term at a cost that exceeds the expected cost from short-term financing, but that provides a full insurance to interest rate risk. Monetary policy and the term structure of interest rates Taken separately monetary policy and term structure modeling are two well-established research areas each comprising a substantial amount of research. But relatively few attempts have been made to integrate the two. The last two chapters of this dissertation take the view that the conduct of monetary policy is an essential element in the determination of the term structure of interest rates, and that explicitly considering the role of amonetary authority in the analysis has a potential of enhancing our understanding of term structure dynamics, and its relation to macro-economic fundamentals in particular. This approach to the term structure is supported by the fact that the analytical framework developed in the literature on optimal monetary policy translates conveniently into a setting well suited for term structure analysis. Chapter 2 makes the point in the simplest setting. A standard model of optimal monetary policy is reformulated in continuous time. Combined with a parameterized form for the market price of risk this produces a standard term structure model with well-known characteristics. This model is estimated on US data for the period 1987 - 2002, treating state variables as latent factors of the term structure. The parameters that are estimated comprise parameters describing the monetary transmission mechanism, parameters describing the monetary authority's preferences and parameters describing the market price of risk. Our estimation technique differs from comparable estimations in the monetary policy literature as these typically take state variables to be directly observable measures of macro-economic aggregates. The results using term structure data are both similar and different to previous findings. The main difference when using term structure data is that the central bank's estimated policy is more aggressive, i.e. more responsive to changes in the underlying state variables.Chapter 3 is devoted to the zero bound on nominal interest rates. While the zero bound is well recognized in the literature on term structure modeling, not much has been said about term structure dynamics under the special circumstance that the short rate is close to zero. I find the optimal monetary policy approach to be particularly well suited for this analysis. The chapter studies a continuous time reduced form version of the monetary transmission mechanism. The monetary authority's optimization problem is formed according to two specifications, interest rate stabilization and interest rate smoothing. For the former the optimization problem is solved analytically, while numerical procedures are adopted forthe latter. The chapter then turns to study implications for the term structure under risk-neutrality. Term structure equations are solved numerically and implications for the term structure are discussed. Data for a low-interest rate country like Japan for 1996 - 2003 exhibits s-shaped yield curves and yield volatility curves. This shape is found to be consistent with a smoothing objective for the short rate. / <p>Diss. Stockholm : Handelshögskolan, 2004</p>