This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.

This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.

This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.

The purpose of this thesis is to examine the nonlinear relationships between financial (and economic) variables within the field of financial econometrics. The thesis comprises two reviews of literatures, one on nonlinear time series models andthe other one on term structure of interest rates, and four empirical essays on financialapplications using nonlinear modelling techniques. The first empirical essay compares different model specifications of a Markov switching CIR model on the term structure of UK interest rates. We find the least restricted model provides the best in-sample estimation results. Although models with restrictive specifications may provide slightly better out-of-sample forecasts in directional movements of the yields, the economic gains seem to be small. In the second essay, we jointly model the nominal and real term structure of the UK interest rates using a three-factor essentially affine no-arbitrage term structure model. The model-implied expected inflation rates are then used in the subsequent analysis on its nonlinear relationship with the FTSE 100 index return premiums, utilizing a smooth transition vector autoregressive model. We find the model implied expected inflation rates remain below the actual inflation rates after the independence of the Bank of England in 1997, and the recent sharp decline of the expected inflation rates may lend support to the standing ground of the central bank for keeping interest rates low. The nonlinearity test on the relationship between the FTSE 100 index return premiums and the expected inflation rates shows that there exists a nonlinear adjustment on the impact from lagged expected inflation rates to current return premiums. The third essay provides us additional insight into the nature of the aggregate stock market volatilities and its relationship to the expected returns, in a Markov switching model framework, using centuries-long aggregate stock market data from six countries (Australia, Canada, Sweden, Switzerland, UK and US). We find that the Markov switching model assuming both regime dependent mean and volatility with a 3-regime specification is capable to captures the extreme movements of the stock market which are short-lived. The volatility feedback effect that we studied on each of these six countries shows a positive sign on anticipating a high volatility regime of the current trading month. The investigation on the coherence in regimes over time for the six countries shows different results for different pairs of countries. In the last essay, we decompose the term premium of the North American CDX investment grade index into a permanent and a stationary component using a Markov switching unobserved component model. We explain the evolution of the two components in relating them to monetary policy and stock market variables. We establish that the inversion of the CDX index term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the risk neutral probability of default in the economy. We find strong evidence that the unprecedented monetary policy response from the Fed during the crisis period was effective in reducing market uncertainty and helped to steepen the term structure of the CDX index, thereby mitigating systemic risk concerns. The impact of stock market volatility on flattening the term premium was substantially more robust in the crisis period. We also show that equity returns make a significant contribution to the CDX term premium over the entire sample period.

A popular class of yield curve models is based on the Nelson and Siegel (1987) (hereafter NS) approach of fitting yield curve data with simple functions of maturity. However, NS models are not theoretically consistent and they also lack an economic foundation, which limits their wider application in finance and economics. This thesis derives an intertemporally-consistent and arbitrage-free version of the NS model, and provides an explicit macroeconomic foundation for that augmented NS (ANS) model. To illustrate the general applicability of the ANS model, it is then applied to four distinct topics spanning finance and economics, each of which are active areas of research in their own right: i.e (1) forecasting the yield curve; (2) investigating relationships between the yield curve and the macroeconomy; (3) fixed interest portfolio management; and (4) investigating the uncovered interest parity hypothesis (UIPH). In each application, the ANS model allows the formal derivation of a parsimonious theoretical framework that captures the essence of the topic under investigation and is readily applicable in practice. Respectively: (1) the intertemporal consistency embedded in the ANS model results in a vector-autoregressive equation that projects the future yield curve from the current yield curve, and forecasts from that model outperform the random-walk benchmark; (2) the economic foundation for the ANS model leads to a single-equation relationship between the current shape of the yield curve and the magnitude and timing of future output growth, and empirical estimations confirm that the theoretical relationship holds in practice; (3) the ANS model provides a theoretically-consistent framework for quantifying risk and returns in fixed interest portfolios, and portfolios optimised ex-ante using that framework outperform a passive benchmark; and (4) the ANS model allows interest rates to be decomposed into a component related to economic fundamentals in the underlying economy, and a component related to cyclical influences. Empirical tests based on the fundamental interest rate components do not reject the UIPH, while the UIPH is rejected based on the cyclical interest rate components. This provides empirical support for suggestions in the theoretical literature that interest rate and exchange rate dynamics associated with cyclical interlinkages between the economy and financial markets under rational expectations may contribute materially to the UIPH puzzle.

This thesis consists of three self-contained papers covering different aspects of public debt management. From a methodological point of view they all have in common that results and models from the theory of finance are used to analyze the effects of public debt management. The first paper, Neutrality of Public Debt Management, studies the case when public debt management does not matter, i.e. when it is neutral. Although strong assumptions are needed to ensure neutrality of public debt management it is nevertheless of interest to study it, since an analysis illuminates the mechanisms through which public debt management affects the economy. The paper starts with a discussion of the assumptions that are needed to ensure neutrality in the models used in the literature. The remainder of the paper tries to relax some of these assumptions. The model employed is an intertemporal general equilibrium model. It is shown that if the agents are identical, public debt is neutral provided the agents pierce the veil of government, and all taxes associated with public debt are lump-sum. It is also shown that if the agents are different but have sufficiently similar utility functions that exhibit hyperbolic absolute risk aversion (i.e., the agents have linear risk tolerance), public debt management is neutral in aggregates, provided the agents pierce the veil of government and all taxes associated with the debt service are lump-sum. This means that public debt management neither affects prices nor aggregate consumption; it might, however affect the individual agent’s consumption-savings decision. Since the class of utility functions that exhibit hyperbolic absolute risk aversion is widely used in economic analysis, this result has several theoretical and empirical implications. The result also has implications for the choice of model in the third paper of the thesis. The second paper, Objectives of Public Debt Management, discusses the objectives of public debt management in an atemporal mean-variance framework. The model employed in this paper differs in one important aspect from the ones previously used in the literature; it takes the firms’ investment decisions into account and hence endogenizes the supply of assets to some extent. It is shown that if the firms’ behavior is introduced, objectives that in the literature have been assumed to stimulate the economic activity do not necessarily have the desired effect. The paper also discusses different objectives aiming at welfare-improvements and economic stimulation. Since the analysis is performed in a unified framework, it is possible to compare the objectives and to discuss their welfare implications. Of particular interest is the welfare aspects of minimization of the costs of public debt. Finally, the paper also discusses the effectiveness of the objectives and it is shown that with one exception, cost minimization, effectiveness declines when the government-issued debt instruments’ share of the asset market falls. The last paper, Public Debt Management and the Term Structure of Interest Rates, develops and uses a stochastic overlapping generations model to analyze the impact of public debt management on the term structure of interest rate. In most of the literature public debt management is thought of as changes in the maturity structure of the outstanding public debt. A change in the maturity structure implies that public debt management affects, e.g., future tax liabilities and hedging opportunities. To capture these effects it is necessary to use an intertemporal framework. In contrast to most models in the literature on public debt management, the model in this paper is intertemporal and takes the general equilibrium effects of public debt management into account, by integrating the financial and real sectors of the economy. This means that current and future asset prices, as well as investments are affected by public debt management. The analysis suggests that it is not the quantities of the long-term and short-term bonds, per se, that determine the effects on the term structure of interest rates. What determines these effects is how public debt management affects the hedging opportunities through changes in asset supply, taxes and prices. / Diss. Stockholm : Handelshögskolan

The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.

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.