The first essay empirically evaluates recently developed techniques that have been proposed to improve the estimation of affine term structure models. The evaluation presented here is performed on two dimensions. On the first dimension, I find that invariant transformations and rotations can be used to reduce the number of free parameters needed to estimate the model and subsequently, improve the empirical performance of affine term structure models. The second dimension of this evaluation surrounds the comparison between estimating an affine term structure model using the model-free method and the inversion method. Using daily LIBOR rate and swap rate quotes from June 1996 to July 2008 to extract a panel of 3,034 time-series observations and 14 cross sections, this paper shows that, a term structure model that is estimated using the model-free method does not perform significantly better in fitting yields, at any horizon, than the more traditional methods available in the literature.The second essay attempts explores implications of using principal components analysis in the estimation of affine term structure models. Early work employing principal component analysis focused on portfolio formation and trading strategies. Recent work, however, has moved the usage of principal components analysis into more formal applications such as the direct involvement of principal component based factors within an affine term structure model. It is this usage of principal components analysis in formal model settings that warrants a study of potential econometric implications of its application to term structure modeling. Serial correlation in interest rate data, for example, has been documented by several authors. The majority of the literature has focused on strong persistence in state variables as giving rise to this phenomena. In this paper, I take yields as given, and hence document the effects of whitening on the model-implied state-dependent factors, subsequently estimated by the principal component based model-free method. These results imply that the process of pre-whitening the data does play a critical role in model estimation. Results are robust to Monte Carlo Simulations. Empirical results are obtained from using daily LIBOR rate and swap rate quotes from June 1996 to July 2008 to extract a panel of zero-coupon yields consisting of 3,034 time-series observations and 14 cross sections.The third essay examines the extent to which the prevalence of estimation risk in numerical integration creates bias, inefficiencies, and inaccurate results in the widely used class of affine term structure models. In its most general form, this class of models relies on the solution to a system of non-linear Ricatti equations to back out the state-factor coefficients. Only in certain cases does this class of models admit explicit, and thus analytically tractable, solutions for the state factor coefficients. Generally, and for more economically plausible scenarios, explicit closed form solutions do not exist and the application of Runge-Kutta methods must be employed to obtain numerical estimates of the coefficients for the state variables. Using a panel of 3,034 yields and 14 cross-sections, this paper examines what perils, if any, exist in this trade off of analytical tractability against economic flexibility. Robustness checks via Monte Carlo Simulations are provided. In specific, while the usage of analytical methods needs less computational time, numerical methods can be used to estimate a broader set of economic scenarios. Regardless of the data generating process, the generalized Gaussian process seems to dominate the Vasicek model in terms of bias and efficiency. However, when the data are generated from a Vasicek model, the Vasicek model performs better than the generalized Gaussian process for fitting the yield curve. These results impart new and important information about the trade off that exists between using analytical methods and numerical methods for estimate affine term structure models.

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.

Estimating risk premia has been at the forefront of the financial economics' literature due to their informational content. Risk premia are of particular interest to academics, policymakers and practitioners given the information they disclose on expected asset returns for a given level of risk, their contribution in asset pricing and their ability to disentangle the different sources of risk. However, risk premia are unobserved and their estimates strongly differ from one study to another, as they are highly sensitive to the specification of the underlying model, sparking hence a strong interest in their analysis. The aim of the thesis is to estimate risk premia in a dynamic term structure model setting. The first part of the thesis comprises of an overview of a particular class of dynamic term structure models, namely affine term structure models. The overview will include important concepts and definitions. The second part of the thesis uses a risk-averse formulation of the uncovered interest rate parity to determine exchange rates through interest rate differentials, and ultimately extract currency risk premia. The method proposed consists of developing an affine Arbitrage-Free class of dynamic Nelson-Siegel term structure models (AFNS) with stochastic volatility to obtain the domestic and foreign discount rate variations, which in turn are used to derive a representation of exchange rate depreciations and risk premia. The third part of the thesis studies both the nominal and real UK term structure of interest rates using a Gaussian dynamic term structure model, which imposes the non-negativity of nominal short maturity rates. Estimates of the term premia, inflation risk premia and market-implied inflation expectations are provided.

Affine term structure models (ATSMs) are one set of popular models for yield curve modeling. Given that the models forecast yields based on the speed of mean reversion, under what circumstances can we distinguish one ATSM from another? The objective of my dissertation is to quantify the benefit of knowing the “true” model as well as the cost of being wrong when choosing between ATSMs. In particular, I detail the power of out-of-sample forecasts to statistically distinguish one ATSM from another given that we only know the data are generated from an ATSM and are observed without errors. My study analyzes the power and size of affine term structure models (ATSMs) by evaluating their relative out-of-sample performance. Essay one focuses on the study of the oneactor ATSMs. I find that the model’s predictive ability is closely related to the bias of mean reversion estimates no matter what the true model is. The smaller the bias of the estimate of the mean reversion speed, the better the out-of-sample forecasts. In addition, my finding shows that the models' forecasting accuracy can be improved, in contrast, the power to distinguish between different ATSMs will be reduced if the data are simulated from a high mean reversion process with a large sample size and with a high sampling frequency. In the second essay, I extend the question of interest to the multiactor ATSMs. My finding shows that adding more factors in the ATSMs does not improve models' predictive ability. But it increases the models' power to distinguish between each other. The multiactor ATSMs with larger sample size and longer time span will have more predictive ability and stronger power to differentiate between models.

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Yes / In this paper, using China’s risk-free and corporate zero yields together with aggregate credit risk measures and various control variables from 2006 to 2013, we document a puzzle of counter-credit-risk corporate yield spreads. We interpret this puzzle as a symptom of the immaturity of China’s credit bond market, which reveals a distorted pricing mechanism latent in the fundamental of this market. We also find interesting results about relationships between corporate yield spreads and interest rates as well as risk premia and the stock index, and these results are somewhat attributed to this puzzle.

The market for interest rate derivatives has in recent decades grown considerably and the need for proper valuation models has increased. Interest rate derivatives are instruments that in some way are contingent on interest rates such as bonds and swaps and most financial transactions are in some way exposed to interest rate risk. Interest rate derivatives are commonly used to hedge this risk. This study focuses on the Black Derman & Toy model and its capability of pricing interest rate derivatives. The purpose was to simulate the model numerically using daily Euro-Bunds and options data to identify if the model can generate accurate prices. A second purpose was to simplify the theory of building a short rate binomial tree, since existing theory explains this step in a complex way. The study concludes that the BDT model have difficulties valuing the extrinsic value of options with longer maturities, especially out-of-the money options.