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| Author | : João Pedro Vidal Nunes |
| Publisher | : |
| Total Pages | : 488 |
| Release | : 2018 |
| Genre | : Equilibrium (Economics) |
| ISBN | : |
| Author | : Arianto Wibowo |
| Publisher | : |
| Total Pages | : 79 |
| Release | : 2006 |
| Genre | : |
| ISBN | : 9789036524421 |
| Author | : Razvan Sufana |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
Dai and Singleton (2000) introduced a typology of affine diffusion models when the domain of admissible values of the factors is an intersection of half planes and under some additional constraints on the parameters. This condition on the domain and the additional sufficient constraints are restrictive and can considerably diminish the practical interest of affine models. In this article we successfully address the research agenda sketched by Duffie, Filipovic, Schachermayer (2003, section 12.2, p. 1042). A systematic investigation is performed and our article provides a complete typology in the two-factor case, without prior restrictions on the domain and on the parameters.
| Author | : Jin-Chuan Duan |
| Publisher | : |
| Total Pages | : |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
This paper proposes a unified state-space formulation for parameter estimation of exponential--affine term structure models. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturity, and can simultaneously deal with many yields on bonds with different maturities. An empirical analysis of two special cases of this general class of model is carried out: the Gaussian case (Vasicek 1977) and the non-Gaussian case (Cox Ingersoll and Ross1985 and Chen and Scott 1992). Our test results indicate a strong rejection of these two cases. A Monte Carlo study indicates that the procedure is reliable for moderate sample sizes.
| Author | : J. Benson Durham |
| Publisher | : |
| Total Pages | : 84 |
| Release | : 2005 |
| Genre | : Econometric models |
| ISBN | : |
Affine term structure models in which the short rate follows a jump-diffusion process are difficult to solve, and the parameters of such models are hard to estimate. Without analytical answers to the partial difference differential equation (PDDE) for bond prices implied by jump-diffusion processes, one must find a numerical solution to the PDDE or exactly solve an approximate PDDE. Although the literature focuses on a single linearization technique to estimate the PDDE, this paper outlines alternative methods that seem to improve accuracy. Also, closed-form solutions, numerical estimates, and closed-form approximations of the PDDE each ultimately depend on the presumed distribution of jump sizes, and this paper explores a broader set of possible densities that may be more consistent with intuition, including a bi-modal Gaussian mixture. GMM and MLE of one- and two-factor jump-diffusion models produce some evidence for jumps, but sensitivity analyses suggest sizeable confidence intervals around the parameters.
| Author | : Damir Filipovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 259 |
| Release | : 2009-07-28 |
| Genre | : Mathematics |
| ISBN | : 3540680152 |
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
| Author | : Wolfgang Lemke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 224 |
| Release | : 2005-12-08 |
| Genre | : Business & Economics |
| ISBN | : 3540283447 |
This book has been prepared during my work as a research assistant at the Institute for Statistics and Econometrics of the Economics Department at the University of Bielefeld, Germany. It was accepted as a Ph.D. thesis titled "Term Structure Modeling and Estimation in a State Space Framework" at the Department of Economics of the University of Bielefeld in November 2004. It is a pleasure for me to thank all those people who have been helpful in one way or another during the completion of this work. First of all, I would like to express my gratitude to my advisor Professor Joachim Frohn, not only for his guidance and advice throughout the com pletion of my thesis but also for letting me have four very enjoyable years teaching and researching at the Institute for Statistics and Econometrics. I am also grateful to my second advisor Professor Willi Semmler. The project I worked on in one of his seminars in 1999 can really be seen as a starting point for my research on state space models. I thank Professor Thomas Braun for joining the committee for my oral examination.
| Author | : Christian Gouriéroux |
| Publisher | : |
| Total Pages | : 66 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
| Author | : Patrick Cheridito |
| Publisher | : |
| Total Pages | : 11 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
Dai and Singleton (2000) study a class of term structure models for interest rates that specify the instantaneous interest rate as an affine combination of the components of an N-dimensional affine diffusion process. Observable quantities of such models are invariant under regular affine transformations of the underlying diffusion process. And in their canonical form, the models in Dai and Singleton (2000) are based on diffusion processes with diagonal diffusion matrices. This motivates the following question: Can the diffusion matrix of an affine diffusion process always be diagonalized by means of a regular affine transformation? We show that if the state space of the diffusion is of the form D = Rm+ x RN - m for integers 0 lt;= m lt;= N satisfying m lt;= 1 or m gt;= N - 1, then there exists a regular affine transformation of D onto itself that diagonalizes the diffusion matrix. On the other hand, we provide examples of affine diffusion processes with state space R2+ x R2 whose diffusion matrices cannot be diagonalized through regular affine transformation.
| Author | : Weijun Yu |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
Abstract: The first part of the dissertation extends some important results in the classical theory of finite dimensional affine processes to infinite dimensional separable Hilbert spaces. In particular, a necessary and sufficient condition for a continuous Markov diffusion process to be affine is given. Based on the extended theory, two affine term structure models are introduced and the existence and uniqueness of the two models are studied. The second part concentrates on a non-linear filtering problem with infinite dimensional observations and the Kushner-Stratonovich equation under the infinite dimensional observation setting is derived. Finally, the obtained results are applied to study the Kalman-Bucy filter with infinite dimensional observations. It is proved that the filter has a Gaussian distribution and the evolution equations of the mean and the covariance of the filter are deduced from the Kushner-Stratonovich equation
