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Affine Multiple Yield Curve Models
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Book Synopsis Affine Multiple Yield Curve Models by : Christa Cuchiero
Download or read book Affine Multiple Yield Curve Models written by Christa Cuchiero and published by . This book was released on 2018 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.
Book Synopsis Analysis of Multi-Factor Affine Yield Curve Models by : Siddhartha Chib
Download or read book Analysis of Multi-Factor Affine Yield Curve Models written by Siddhartha Chib and published by . This book was released on 2008 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In finance and economics, there is a great deal of work on the theoretical modeling and statistical estimation of the yield curve (defined as the relation between $- frac{1}{ tau } log p_{t}( tau )$ and $ tau$, where $p_{t}( tau )$ is the time $t$ price of the zero-coupon bond with payoff 1 at maturity date $t tau$). Of much current interest are models in which the bond prices are derived from a stochastic discount factor (SDF) approach that enforces an important no-arbitrage condition. The log of the SDF is assumed to be an affine function of latent and observed factors, where these factors are assumed to follow a stationary Markov process. In this paper we revisit the question of how such multi-factor affine models of the yield curve should be fit. Our discussion, like that of cite% {AngDongPiazzesi07}, is from the Bayesian MCMC viewpoint, but our implementation of this viewpoint is different and novel. Key aspects of the inferential framework include (i) a prior on the parameters of the model that is motivated by economic considerations, in particular, those involving the slope of the implied yield curve; (ii) posterior simulation of the parameters in ways to improve the efficiency of the MCMC output, for example, through sampling of the parameters marginalized over the factors, and through tailoring of the proposal densities in the Metropolis-Hastings steps using information about the mode and curvature of the current target based on the output of a simulating annealing algorithm; and (iii) measures to mitigate numerical instabilities in the fitting through reparameterizations and square root filtering recursions. We apply the techniques to explain the monthly yields on nine US Treasuries (with maturities ranging from 1 to 120 months) over the period January 1986 to December 2005. The model contains three factors, one latent and two observed. We also consider the problem of predicting the nine yields for each month of 2006. We show that the (multi-step ahead) prediction regions properly bracket the actual yields in those months, thus highlighting the practical value of the fitted model.
Book Synopsis Yield Curve Modeling and Forecasting by : Francis X. Diebold
Download or read book Yield Curve Modeling and Forecasting written by Francis X. Diebold and published by Princeton University Press. This book was released on 2013-01-15 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A General HJM Framework for Multiple Yield Curve Modeling by : Christa Cuchiero
Download or read book A General HJM Framework for Multiple Yield Curve Modeling written by Christa Cuchiero and published by . This book was released on 2015 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.
Book Synopsis Machine Learning for Multiple Yield Curve Markets by : Sandrine Gümbel
Download or read book Machine Learning for Multiple Yield Curve Markets written by Sandrine Gümbel and published by . This book was released on 2020 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian process regression, a machine learning methodology having many similarities with extended Kalman filtering - a technique which has been applied many times to interest rate markets and term structure models. We find very good results for the single curve markets and many challenges for the multi curve markets in a Vasicek framework. The Gaussian process regression is implemented with the Adam optimizer and the non-linear conjugate gradient method, where the latter performs best. We also point towards future research.
Book Synopsis Yield Curve Modeling by : Y. Stander
Download or read book Yield Curve Modeling written by Y. Stander and published by Springer. This book was released on 2005-06-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will give the reader insight into how to model yield curves in our incomplete and imperfect financial markets. An extensive list of yield curve models are shown and discussed. Using actual market instruments, these models are then applied and the different yield curves are compared. It is assumed that the reader has a basic understanding of the financial instruments available in the market. Various issues that have to be taken into account in practice are discussed, like daycount conventions, business-day rules, the credit quality of the instrument and liquidity to name but a few. It is also shown how yield curves can be used to estimate credit spreads and country risk premiums. Creating a yield curve model has some implications in risk management. Specifically - the model, operational, liquidity and basis risks are discussed.
Book Synopsis Yield Curves and Forward Curves for Diffusion Models of Short Rates by : Gennady A. Medvedev
Download or read book Yield Curves and Forward Curves for Diffusion Models of Short Rates written by Gennady A. Medvedev and published by Springer. This book was released on 2019-05-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.
Book Synopsis Yield Curve Dynamics by : Ronald J. Ryan
Download or read book Yield Curve Dynamics written by Ronald J. Ryan and published by Global Professional Publishi. This book was released on 1997 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: � Invaluable to financial professionals � Breakthrough that examines both theory and practical solutions Examines both the advanced theory and practice of these techniques. Topics include: single- and multi-factor models; applying yield-curve modeling to risk management; forecasting short-term interest rates; unique yield-curve volatility; and trading strategies.
Book Synopsis Interest Rate Modeling by : Lixin Wu
Download or read book Interest Rate Modeling written by Lixin Wu and published by CRC Press. This book was released on 2019-03-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Features Presents a complete cycle of model construction and applications, showing readers how to build and use models Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments Contains exercise sets and a number of examples, with many based on real market data Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.
Book Synopsis Developments in Macro-Finance Yield Curve Modelling by : Jagjit S. Chadha
Download or read book Developments in Macro-Finance Yield Curve Modelling written by Jagjit S. Chadha and published by Cambridge University Press. This book was released on 2014-02-06 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art research from academics and policymakers on the role of and challenges to monetary policy during the ongoing financial crisis.
Book Synopsis Handbook of Computational Finance by : Jin-Chuan Duan
Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Book Synopsis Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration by :
Download or read book Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Interest Rate Modeling by : Leif B. G. Andersen
Download or read book Interest Rate Modeling written by Leif B. G. Andersen and published by . This book was released on 2010 with total page 1154 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The three volumes of Interest rate modeling are aimed primarily at practitioners working in the area of interest rate derivatives, but much of the material is quite general and, we believe, will also hold significant appeal to researchers working in other asset classes. Students and academics interested in financial engineering and applied work will find the material particularly useful for its description of real-life model usage and for its expansive discussion of model calibration, approximation theory, and numerical methods."--Preface.
Book Synopsis Fixed Income Modelling by : Claus Munk
Download or read book Fixed Income Modelling written by Claus Munk and published by Oxford University Press. This book was released on 2011-06-30 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large number of securities related to various interest rates are traded in financial markets. Traders and analysts in the financial industry apply models based on economics, mathematics and probability theory to compute reasonable prices and risk measures for these securities. This book offers a unified presentation of such models and securities.
Book Synopsis Two Essays on Estimation and Inference of Affine Term Structure Models by : Qian Wang
Download or read book Two Essays on Estimation and Inference of Affine Term Structure Models written by Qian Wang and published by . This book was released on 2015 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine term structure models (ATSMs) are one set of popular models for yield curve modeling. Given that the models forecast yields based on the speed of mean reversion, under what circumstances can we distinguish one ATSM from another? The objective of my dissertation is to quantify the benefit of knowing the “true” model as well as the cost of being wrong when choosing between ATSMs. In particular, I detail the power of out-of-sample forecasts to statistically distinguish one ATSM from another given that we only know the data are generated from an ATSM and are observed without errors. My study analyzes the power and size of affine term structure models (ATSMs) by evaluating their relative out-of-sample performance. Essay one focuses on the study of the one-factor ATSMs. I find that the model’s predictive ability is closely related to the bias of mean reversion estimates no matter what the true model is. The smaller the bias of the estimate of the mean reversion speed, the better the out-of-sample forecasts. In addition, my finding shows that the models' forecasting accuracy can be improved, in contrast, the power to distinguish between. different ATSMs will be reduced if the data are simulated from a high mean reversion process with a large sample size and with a high sampling frequency. In the second essay, I extend the question of interest to the multi-factor ATSMs. My finding shows that adding more factors in the ATSMs does not improve models' predictive ability. But it increases the models' power to distinguish between each other. The multi-factor ATSMs with larger sample size and longer time span will have more predictive ability and stronger power to differentiate between models.
Book Synopsis Perturbation Methods in Credit Derivatives by : Colin Turfus
Download or read book Perturbation Methods in Credit Derivatives written by Colin Turfus and published by John Wiley & Sons. This book was released on 2021-03-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume Perturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources. The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including: Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently Developing more efficient algorithms for generating stress scenarios for market risk quants Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.
Book Synopsis Interest Rate Modeling: Post-Crisis Challenges and Approaches by : Zorana Grbac
Download or read book Interest Rate Modeling: Post-Crisis Challenges and Approaches written by Zorana Grbac and published by Springer. This book was released on 2015-12-26 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling a gap in the literature caused by the recent financial crisis, this book provides a treatment of the techniques needed to model and evaluate interest rate derivatives according to the new paradigm for fixed income markets. Concerning this new development, there presently exist only research articles and two books, one of them an edited volume, both being written by researchers working mainly in practice. The aim of this book is to concentrate primarily on the methodological side, thereby providing an overview of the state-of-the-art and also clarifying the link between the new models and the classical literature. The book is intended to serve as a guide for graduate students and researchers as well as practitioners interested in the paradigm change for fixed income markets. A basic knowledge of fixed income markets and related stochastic methodology is assumed as a prerequisite.
