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.

No description available.

Thesis (Ph.D.)--University of Western Australia, 2006.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Anderson, Dr. David V.; Committee Member: Hasler, Dr. Paul E.; Committee Member: Mooney, Dr. Vincent J.; Committee Member: Taylor, Dr. David G.; Committee Member: Vuduc, Dr. Richard.

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

In this thesis, we study locally strictly convex surfaces from the affine differential viewpoint and generalize some tools for locally strictly submanifolds of codimension 2. We introduce a family of affine metrics on a locally strictly convex surface M in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if M is immersed in a locally atrictly convex hyperquadric, then the symmetric and the antisymmetric planes coincide and contain the affine normal to the hyperquadric. In particular, any surface immersed in a locally strictly convex hyperquadric is affine semiumbilical with respect to the symmetric or antisymmetric equiaffine planes. More generally, by using the metric of the transversal vector field on M we introduce the affine normal plane and the families of the affine distance and height functions on M. We show that the singularities of the family of the affine height functions appear at directions on the affine normal plane and the singularities of the family of the affine distance functions appear at points on the affine normal plane and the affine focal points correspond as degenerate singularities of the family of affine distance functions. Moreover we show that if M is immersed in a locally strictly convex hypersurface then the affine normal plane contains the affine normal vector to the hypersurface. Finally, we conclude that any surface immersed in a locally strictly convex hypersphere is affine semiumbilical. / Nesta tese estudamos as superfícies localmente estritamente convexas desde o ponto de vista da geometria diferencial afim e generalizamos algumas ferramentas para subvariedades localmente estritamente convexas de codimensão 2. Introduzimos uma família de métricas afins sobre uma superfície localmente estritamente convexa M no 4-espaço afim. Então, definimos os planos equiafins simétrico e antissimétrico associados com alguma métrica. Mostramos que se M é imersa em uma hiperquádrica localmente estritamente convexa, então os planos simétrico e assimétrico são iguais e contêm o campo vetorial normal afim à hiperquádrica. Em particular, qualquer superfície imersa em uma hiperquádrica localmente estritamente convexa é semiumbílica afim com relação ao plano equiafim simétrico ou antissimétrico. Mais geralmente, usando a métrica do campo transversal sobre M introduzimos o plano normal afim e as famílias de funções distância e altura afim sobre M. Provamos que as singularidades da família de funções altura afim aparecem como direções do plano normal afim e as singularidades da família de funções distância afim aparecem como pontos sobre o plano normal afim e os pontos focais correspondem às singularidades degeneradas da família de funções distância afim. Também provamos que se M é uma superfície imersa em uma hipersuperfície localmente estritamente convexa, então o plano normal afim contém o vetor normal afim à hipersuperfície. Finalmente, concluímos que qualquer superfície imersa em uma hiperesfera localmente estritamente convexa é semiumbílica afim.

This work presents a class of models in asset pricing, whose underlying has dynamics of Affine jump diffusion type. We first present L´evy processes with their properties. We then introduce Affine jump diffusion processes which are basically a particular class of L´evy processes. Our motivation for these is driven by the fact that many financial models are built on them. Affine jump diffusion processes present good analytical properties that allow one to get close form formulas for a wide range of option pricing. The approach we use here is based on the paper by Duffie D, Pan J, and Singleton K. An example will show how incorporating parameters such as the volatility of the underlying asset in the model, can influence the resulting price of the financial instrument under consideration. We will also show how this class of models incorporate well known models, specially those used to model interest rates dynamics, like for instance the Vasicek model. / Dissertation (MSc (Mathematics of Finance))--University of Pretoria, 2008. / Mathematics and Applied Mathematics / unrestricted

No description available.

In this thesis, we study locally strictly convex surfaces from the affine differential viewpoint and generalize some tools for locally strictly submanifolds of codimension 2. We introduce a family of affine metrics on a locally strictly convex surface M in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if M is immersed in a locally atrictly convex hyperquadric, then the symmetric and the antisymmetric planes coincide and contain the affine normal to the hyperquadric. In particular, any surface immersed in a locally strictly convex hyperquadric is affine semiumbilical with respect to the symmetric or antisymmetric equiaffine planes. More generally, by using the metric of the transversal vector field on M we introduce the affine normal plane and the families of the affine distance and height functions on M. We show that the singularities of the family of the affine height functions appear at directions on the affine normal plane and the singularities of the family of the affine distance functions appear at points on the affine normal plane and the affine focal points correspond as degenerate singularities of the family of affine distance functions. Moreover we show that if M is immersed in a locally strictly convex hypersurface then the affine normal plane contains the affine normal vector to the hypersurface. Finally, we conclude that any surface immersed in a locally strictly convex hypersphere is affine semiumbilical. / Nesta tese estudamos as superfícies localmente estritamente convexas desde o ponto de vista da geometria diferencial afim e generalizamos algumas ferramentas para subvariedades localmente estritamente convexas de codimensão 2. Introduzimos uma família de métricas afins sobre uma superfície localmente estritamente convexa M no 4-espaço afim. Então, definimos os planos equiafins simétrico e antissimétrico associados com alguma métrica. Mostramos que se M é imersa em uma hiperquádrica localmente estritamente convexa, então os planos simétrico e assimétrico são iguais e contêm o campo vetorial normal afim à hiperquádrica. Em particular, qualquer superfície imersa em uma hiperquádrica localmente estritamente convexa é semiumbílica afim com relação ao plano equiafim simétrico ou antissimétrico. Mais geralmente, usando a métrica do campo transversal sobre M introduzimos o plano normal afim e as famílias de funções distância e altura afim sobre M. Provamos que as singularidades da família de funções altura afim aparecem como direções do plano normal afim e as singularidades da família de funções distância afim aparecem como pontos sobre o plano normal afim e os pontos focais correspondem às singularidades degeneradas da família de funções distância afim. Também provamos que se M é uma superfície imersa em uma hipersuperfície localmente estritamente convexa, então o plano normal afim contém o vetor normal afim à hipersuperfície. Finalmente, concluímos que qualquer superfície imersa em uma hiperesfera localmente estritamente convexa é semiumbílica afim.