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Author : Belinda O'Connor
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (969 download)
Download or read book The Heath-Jarrow-Morton Model for the Term Structure of Interest Rates written by Belinda O'Connor and published by . This book was released on 2000 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rajna Gibson
Publisher : Now Publishers Inc
ISBN 13 : 1601983727
Total Pages : 171 pages
Book Rating : 4.6/5 (19 download)
Download or read book Modeling the Term Structure of Interest Rates written by Rajna Gibson and published by Now Publishers Inc. This book was released on 2010 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.
Author : Damir Filipovic
Publisher : Springer
ISBN 13 : 354044548X
Total Pages : 141 pages
Book Rating : 4.5/5 (44 download)
Download or read book Consistency Problems for Heath-Jarrow-Morton Interest Rate Models written by Damir Filipovic and published by Springer. This book was released on 2004-11-02 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.
Author : Damir Filipovic
Publisher : Springer Science & Business Media
ISBN 13 : 3540680152
Total Pages : 259 pages
Book Rating : 4.5/5 (46 download)
Download or read book Term-Structure Models written by Damir Filipovic and published by Springer Science & Business Media. This book was released on 2009-07-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Przemyslaw Repetowicz
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (129 download)
Download or read book Modelling the Term Structure of Interest Rates a La Heath-Jarrow-Morton But with Non-Gaussian Fluctuations written by Przemyslaw Repetowicz and published by . This book was released on 2009 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a generalization of the Heath-Jarrow-Morton model for the term structure of interest rates where the forward rate is driven by Paretian fluctuations. We derive a generalization of Ito's lemma for the calculation of a differential of a Paretian stochastic variable and use it to derive a Stochastic Differential Equation for the discounted bond price.We show that it is not possible to choose the parameters of the model to ensure absence of drift of the discounted bond price. Then we consider a Continuous Time Random Walk with jumps driven by Paretian random variables and we derive the large time scaling limit of the jump probability distribution function (pdf). We show that under certain conditions defined in text the large time scaling limit of the jump pdf in the Fourier domain is tilde{ omega}_t(k,t) sim exp{ - mathfrak{K}/( ln(k t))^2 } and is different from the case of a random walk with Gaussian fluctuations.
Author : Andrew Mark Jeffrey
Publisher :
ISBN 13 :
Total Pages : 604 pages
Book Rating : 4.:/5 (222 download)
Download or read book Essays on the Term Structure of Interest Rates Within the Heath-Jarrow-Morton Framework written by Andrew Mark Jeffrey and published by . This book was released on 1997 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maria Krivko
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (86 download)
Download or read book Numerical Methods for Heath-Jarrow-Morton Model of Interest Rates written by Maria Krivko and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The celebrated HJM framework models the evolution of the term structure of interest rates through the dynamics of the forward rate curve. These dynamics are described by a multifactor infinite-dimensional stochastic equation with the entire forward rate curve as state variable. Under no-arbitrage conditions, the HJM model is fully characterized by specifying forward rate volatility functions and the initial forward curve. In short, it can be described as a unifying framework with one of its most striking features being the generality: any arbitrage-free interest rate model driven by Brownian motion can be described as a special case of the HJM model. The HJM model has closed-form solutions only for some special cases of volatility, and valuations under the HJM framework usually require a numerical approximation. We propose and analyze numerical methods for the HJM model. To construct the methods, we first discretize the infinite-dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite-dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense. The proposed numerical algorithms are highly computationally efficient due to the use of high-order quadrature rules which allow us to take relatively large discretization steps in the maturity time without affecting overall accuracy of the algorithms. They also have a high degree of flexibility and allow to choose appropriate approximations in maturity and calendar times separately. Convergence theorems for the methods are proved. Results of some numerical experiments with European-type interest rate derivatives are presented.
Author : Ramaprasad Bhar
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (249 download)
Download or read book Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems written by Ramaprasad Bhar and published by . This book was released on 2000 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ramaprasad Bhar
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (129 download)
Download or read book Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems written by Ramaprasad Bhar and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a Heath-Jarrow-Morton models for the term structure of interest rates in which the forward rate volatility is a function of the instantaneous spot rate of interest, a set of dicrete forward rates and time to maturity of the bond. We show how the stochastic dynamics may be expressed as a system of Markovian stochastic differential equations. We obtain the partial differential equation which allows the pricing of contingent claims in this framework.
Author : Takashi Yasuoka
Publisher : Bentham Science Publishers
ISBN 13 : 1681081261
Total Pages : 302 pages
Book Rating : 4.6/5 (81 download)
Download or read book Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk written by Takashi Yasuoka and published by Bentham Science Publishers. This book was released on 2015-10-13 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest Rate Modeling for Risk Management introduces a theoretical framework - the ‘real-world’ model - that allows us to estimate the market price of interest rate risk based on practical and real life situations. The model can be briefly summarized as a process of estimating the market prices of risk through discretization of forward rates with a ‘space-state setup’ whilst considering historical data trends. The book starts with a brief explanation of interest rate stochastic analysis fundamentals before delving into standard models such as Heath-Jarrow-Morton, Hull-White and LIBOR models. The real-world model is then explained in subsequent chapters while applying different frameworks. Additionally, the book also explains some properties of the real-world model, along with the negative price tendency of the market price for risk and a positive market price for risk (with an example of this actually occurring). Readers will also find a handy appendix with proofs to complement the numerical methods explained in the book. This book is intended as a primer for practitioners in financial institutions involved in interest rate risk management. It also presents a new perspective for researchers and graduates in econometrics and finance on the study of interest rate models.
Author : Klaus Sandmann
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (535 download)
Download or read book Closed Form Term Structure Derivatives in a Heath-Jarrow Morton Model with Log-normal Annually Compounded Interest Rates written by Klaus Sandmann and published by . This book was released on 1994 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrew Jeffrey
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics written by Andrew Jeffrey and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the class of Heath-Jarrow-Morton term structure models where the spot interest rate is Markov and the term structure at time t is a function of time, maturity and the spot interest rate at time t. A representation for this class of models is derived and I show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen. I provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable. I also derive a partial differential equation representation of the term structure dynamics which does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process. Using the analysis presented in this paper a class of intertemporal term structure models is derived.
Author : Klaus Sandmann
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (755 download)
Download or read book Closed form term structure derivates in a Heath-Jarrow-Morton model with log-normal annually compounded interest rates written by Klaus Sandmann and published by . This book was released on 1994 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leonard Tchuindjo
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Factors' Correlation in the Heath-Jarrow-Morton Interest Rate Model written by Leonard Tchuindjo and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new derivation of the Heath-Jarrow-Morton risk-neutral drift restriction that takes into account nonzero instantaneous correlations between factors. The result allows avoiding the orthogonalization of factors and provides an approach by which interest rate derivatives can be priced by preserving the economic meaning of each underlying factor. An application is given for the term structure of creditrisky bonds, driven by two correlated factors -- the risk-free forward rate and the forward credit spreads.
Author : Andrew Jeffrey
Publisher :
ISBN 13 : 9780947069216
Total Pages : 34 pages
Book Rating : 4.0/5 (692 download)
Download or read book Construction of a Single Factor Heath-Jarrow-Morton Term Structure Model written by Andrew Jeffrey and published by . This book was released on 1994 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Jarrow
Publisher : CRC Press
ISBN 13 : 9781032475264
Total Pages : 0 pages
Book Rating : 4.4/5 (752 download)
Download or read book Modeling Fixed Income Securities and Interest Rate Options written by Robert Jarrow and published by CRC Press. This book was released on 2023-01-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling Fixed Income Securities and Interest Rate Options offers several new updates. The new edition of the classic textbook presents the basics of fixed-income securities. It requires a minimum of prerequisites. The author presents a coherent theoretical framework for understanding all basic models.
Author : René Carmona
Publisher : Springer Science & Business Media
ISBN 13 : 3540270671
Total Pages : 236 pages
Book Rating : 4.5/5 (42 download)
Download or read book Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
