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Author: Michael Henseler Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
We present an affine arbitrage-free dynamic term-structure model based on a representation of instantaneous forward rates as sum of exponentials. The model, which is Gaussian and belongs to the class of Heath-Jarrow-Morton-type models, is intuitively appealing as a suitable linear combination of the stochastic factors can be interpreted as stochastic evolution of stable principal components of the yield curve. Focusing on applications, we derive general principal components in such an affine-linear model, calibrate the model to government bond prices, and derive simple formulas to price caps and floors.
Author: Michael Henseler Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
We present an affine arbitrage-free dynamic term-structure model based on a representation of instantaneous forward rates as sum of exponentials. The model, which is Gaussian and belongs to the class of Heath-Jarrow-Morton-type models, is intuitively appealing as a suitable linear combination of the stochastic factors can be interpreted as stochastic evolution of stable principal components of the yield curve. Focusing on applications, we derive general principal components in such an affine-linear model, calibrate the model to government bond prices, and derive simple formulas to price caps and floors.
Author: Lin Chen Publisher: Springer Science & Business Media ISBN: 364246825X Category : Business & Economics Languages : en Pages : 158
Book Description
There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc ture consistent with the initial tenn structure data.
Author: Damir Filipovic Publisher: Springer Science & Business Media ISBN: 3540680152 Category : Mathematics Languages : en Pages : 259
Book Description
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: David Jamieson Bolder Publisher: ISBN: Category : Languages : en Pages : 89
Book Description
Modelling term-structure dynamics is an important component in measuring and managing the exposure of portfolios to adverse movements in interest rates. Model selection from the enormous term-structure literature is far from obvious and, to make matters worse, a number of recent papers have called into question the ability of some of the more popular models to adequately describe interest rate dynamics. The author, in attempting to find a relatively simple term-structure model that does a reasonable job of describing interest rate dynamics for risk-management purposes, examines two sets of models. The first set involves variations of the Gaussian affine term-structure model by modestly building on the recent work of Dai and Singleton (2000) and Duffee (2002). The second set includes and extends Diebold and Li (2003). After working through the mathematical derivation and estimation of these models, the author compares and contrasts their performance on a number of in- and out-of-sample forecasting metrics, their ability to capture deviations from the expectations hypothesis, and their predictions in a simple portfolio-optimization setting. He finds that the extended Nelson-Siegel model and an associated generalization, what he terms the exponential-spline model, provide the most appealing modelling alternatives when considering the various model criteria.
Author: Francis X. Diebold Publisher: Princeton University Press ISBN: 0691146802 Category : Business & Economics Languages : en Pages : 223
Book Description
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.
Author: Sandrine Gümbel Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Dariusz Gatarek Publisher: John Wiley & Sons ISBN: 0470060417 Category : Business & Economics Languages : en Pages : 290
Book Description
The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.
Author: Frank J. Fabozzi, CFA Publisher: John Wiley & Sons ISBN: 9781883249175 Category : Business & Economics Languages : en Pages : 408
Book Description
Advances in Fixed Income Valuation Modeling and Risk Management provides in-depth examinations by thirty-one expert research and opinion leaders on topics such as: problems encountered in valuing interest rate derivatives, tax effects in U.S. government bond markets, portfolio risk management, valuation of treasury bond futures contract's embedded options, and risk analysis of international bonds.
Author: Marco Corazza Publisher: Springer Nature ISBN: 3030789659 Category : Business & Economics Languages : en Pages : 389
Book Description
The cooperation and contamination between mathematicians, statisticians and econometricians working in actuarial sciences and finance is improving the research on these topics and producing numerous meaningful scientific results. This volume presents new ideas, in the form of four- to six-page papers, presented at the International Conference eMAF2020 – Mathematical and Statistical Methods for Actuarial Sciences and Finance. Due to the now sadly famous COVID-19 pandemic, the conference was held remotely through the Zoom platform offered by the Department of Economics of the Ca’ Foscari University of Venice on September 18, 22 and 25, 2020. eMAF2020 is the ninth edition of an international biennial series of scientific meetings, started in 2004 at the initiative of the Department of Economics and Statistics of the University of Salerno. The effectiveness of this idea has been proven by wide participation in all editions, which have been held in Salerno (2004, 2006, 2010 and 2014), Venice (2008, 2012 and 2020), Paris (2016) and Madrid (2018). This book covers a wide variety of subjects: artificial intelligence and machine learning in finance and insurance, behavioral finance, credit risk methods and models, dynamic optimization in finance, financial data analytics, forecasting dynamics of actuarial and financial phenomena, foreign exchange markets, insurance models, interest rate models, longevity risk, models and methods for financial time series analysis, multivariate techniques for financial markets analysis, pension systems, portfolio selection and management, real-world finance, risk analysis and management, trading systems, and others. This volume is a valuable resource for academics, PhD students, practitioners, professionals and researchers. Moreover, it is also of interest to other readers with quantitative background knowledge.
Author: Michael Henseler
Author: Michael Henseler
Author: Lin Chen
Author: Damir Filipovic
Author: David Jamieson Bolder
Author: Francis X. Diebold
Author: Sandrine Gümbel
Author: Dariusz Gatarek
Author: Kevin C. Ahlgrim
Author: Frank J. Fabozzi, CFA
Author: Marco Corazza