Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling

Understanding the dynamic evolution of the yield curve is critical to many financial tasks, including pricing financial assets and their derivatives, managing financial risk, allocating portfolios, structuring fiscal debt, conducting monetary policy, and valuing capital goods. Unfortunately, most yield curve models tend to be theoretically rigorous but empirically disappointing, or empirically successful but theoretically lacking. In this book, Francis Diebold and Glenn Rudebusch propose two extensions of the classic yield curve model of Nelson and Siegel that are both theoretically rigorous and empirically successful. The first extension is the dynamic Nelson-Siegel model (DNS), while the second takes this dynamic version and makes it arbitrage-free (AFNS). Diebold and Rudebusch show how these two models are just slightly different implementations of a single unified approach to dynamic yield curve modeling and forecasting. They emphasize both descriptive and efficient-markets aspects, they pay special attention to the links between the yield curve and macroeconomic fundamentals, and they show why DNS and AFNS are likely to remain of lasting appeal even as alternative arbitrage-free models are developed. Based on the Econometric and Tinbergen Institutes Lectures, Yield Curve Modeling and Forecasting contains essential tools with enhanced utility for academics, central banks, governments, and industry.

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.

In this note we consider a classical term structure model framework, that is, a HJM framework on a time-discrete tenor, like the LIBOR market model, using a sequence of tenor discretization, where the tenors are valid for a specific simulation time interval.The setup then allows to model dynamic refinements of the tenor structure and, as a special case, a quasi time-homogenous tenor structure.A time-homogenous tenor structure has some relevance in exposure simulations, where two requirements come together: it is desirable to model a finer tenor structure on the short end of the rate curve compared to the long end of the rate curve and, this property should persist in the simulation at a future time.The property is easily fulfilled by models, which uses an equally fine discretization at all times, e.g., a short rate model, where simulation time discretization and tenor time discretization coincide.As we will demonstrate, a refinement of the tenor structure via a simple interpolation of forward rates would either introduce a strong restriction on the model's volatility structure (as it is the case for a classical fixed tenor LIBOR market model) or introduce an arbitrage violation. The challenge in the refinement is to simulate the right stochastic drifts. Under a (milder) condition on the model's volatility structure, the drifts can be reconstructed using a single additional state variable. The additional state variable is only needed on the coarse discretization tenors, limiting the computational resources needed to implement the model.In a limit case, the approach can be used to glue together a short rate model for the short end of the rate curve and a term-structure model for the long end of the rate curve in a time-homogenous way.

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.

Abstract: This thesis is devoted to the study of term structure modeling in interest rate markets and defaultable term structure modeling in credit risk markets. Post-crisis interest rate markets possess two main characteristics: multiple curves and discontinuities. While a lot of effort has been put in the study of the former, there is one crucial feature of discontinuities, which we will call stochastic. discontinuities, whose investigation seems to be lacking in the interest rate literature so far. This concept of discontinuities has recently been studied in a credit risk framework in Fontana and Schmidt (2018) and Gehmlich and Schmidt (2018). Stochastic discontinuities describe jumps in the underlying interest rates or processes depicting events occurring at announced dates but with a possibly unanticipated outcome. This type of events is clearly present in interest rates, as can be evidenced by jumps in the underlying rates in correspondence with meetings of the European Central Bank. We provide a general analysis of the term structure modeling of multiple curves with the presence of stochastic discontinuities and derive conditions to ensure absence of arbitrage. In particular, we provide an extended Heath-Jarrow-Morton formulation with semimartingales as driving processes. Beyond that, a general market model approach is investigated and some insightful examples in an affine framework are presented in order to show the potential of this approach. Bond prices are calibrated in a Vasi cek framework by means of machine learning techniques adapted to Gaussian processes. In credit risk we are concerned with securities that are subject to default risk. We present a general analysis of the term structure modeling of defaultable bonds allowing for discontinuities. In particular, we derive conditions to ensure absence of arbitrage in the credit risky financial market in an extended Heath-Jarrow-Morton framework with semimartingales as driving processes. We provide a similar characterization for defaultable bonds with recovery.

This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.

The paper assesses estimates of term structure models for the United States. To this end, this paper first describes the mathematics underlying two types of term structure models, namely the Nelson-Siegel and Cox, Ingersoll and Ross family of models, and the estimation techniques. It then presents estimations of some of specific models within these families of models?three-factor Nelson-Siegel Model, four-factor Svensson model, and preference-free, two-factor Cox, Ingersoll and Roll model?for the United States from 1972 to mid 2011. It subsequently provides an assessment of the estimations. It concludes that these estimations of the term structure models successfully capture the dynamics of the term structure in the United States.