Dynamic Term Structure Models

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

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. Taken together, our results shed new light on estimation and interpretation of GDTSMs, as well as the eff ects of di fferent specifi cations of the risk premiums and the risk-neutral distribution of bond yields on the observed dynamics of the yield curve.

This paper gives a new taxonomy of dynamic term structure models that classifies all existing TSMs as either fundamental models or preference-free single-plus, double-plus, and triple-plus models. We exemplify the new taxonomy by considering preference-free versions of some well-known fundamental short rate models. Single-plus extensions of the fundamental models are shown to be both time-homogeneous and preference-free - two characteristics which do not simultaneously hold under any existing class of TSMs. Though the analytical apparatus for pricing fixed income securities is identical under fundamental models and single-plus models, the latter models are consistent with general non-linear forms of MPRs which may also depend upon an arbitrary set of state variables, leading to better estimates of risk-neutral parameters. The preference-free double-plus and triple-plus extensions of the fundamental models are similar to the Heath, Jarrow, and Morton [1992] models, in that time-inhomogeneous drifts and volatilities are used as quot;smoothing variablesquot; to fit the initial bond prices and initial term structure of volatilities, respectively.

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.

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 paper develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counter parts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk curren;t, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditionallikelihood functions for coupon bond yields for the resulting nonlinear models under thehistorical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its out-of-sampleforecasting performance.

This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

The affine dynamic term structure model (DTSM) is the canonical empirical finance representation of the yield curve. However, the possibility that DTSM estimates may be distorted by small-sample bias has been largely ignored. We show that conventional estimates of DTSM coefficients are indeed severely biased, and this bias results in misleading estimates of expected future short-term interest rates and of long-maturity term premia. We provide a variety of bias-corrected estimates of affine DTSMs, both for maximally flexible and over-identified specifications. Our estimates imply short rate expectations and term premia that are more plausible from a macro-finance perspective.