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.

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.

This paper discusses the estimation of models of the term structure of interest rates. After reviewing the term structure models, specifically the Nelson-Siegel Model and Affine Term- Structure Model, this paper estimates the terms structure of Treasury bond yields for the United States with pre-crisis data. This paper uses a software developed by Fund staff for this purpose. This software makes it possible to estimate the term structure using at least nine models, while opening up the possibility of generating simulated paths of the term structure.

A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape. Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature: • An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them • Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments • Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints • The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility • Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds • Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing • Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints • Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets. Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.

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.

This book covers the latest theories and empirical findings of financial risk, its measurement and management, and its applications in the world of finance.

The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.