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Modelling The Term Structure Of Interest Rates A La Heath Jarrow Morton But With Non Gaussian Fluctuations
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Book Synopsis Modelling the Term Structure of Interest Rates a La Heath-Jarrow-Morton But with Non-Gaussian Fluctuations by : Przemyslaw Repetowicz
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.
Book Synopsis Consistency Problems for Heath-Jarrow-Morton Interest Rate Models by : Damir Filipovic
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.
Book Synopsis Modeling the Term Structure of Interest Rates by : Rajna Gibson
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.
Book Synopsis The Heath-Jarrow-Morton Model for the Term Structure of Interest Rates by : Belinda O'Connor
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:
Book Synopsis Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems by : Ramaprasad Bhar
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:
Book Synopsis Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems by : Ramaprasad Bhar
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.
Book Synopsis Numerical Methods for Heath-Jarrow-Morton Model of Interest Rates by : Maria Krivko
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.
Book Synopsis Closed form term structure derivates in a Heath-Jarrow-Morton model with log-normal annually compounded interest rates by : Klaus Sandmann
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:
Book Synopsis Dynamic Term Structure Modeling Beyond the Paradigm of Absolute Continuity by : Sandrine Gümbel
Download or read book Dynamic Term Structure Modeling Beyond the Paradigm of Absolute Continuity written by Sandrine Gümbel and published by . This book was released on 2019* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics by : Andrew Jeffrey
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.
Book Synopsis Essays on the Term Structure of Interest Rates Within the Heath-Jarrow-Morton Framework by : Andrew Mark Jeffrey
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:
Book Synopsis Empirical Comparisons of One Factor Heath-Jarrow-Morton Term Structure Models by : Robert A. J. Gibson
Download or read book Empirical Comparisons of One Factor Heath-Jarrow-Morton Term Structure Models written by Robert A. J. Gibson and published by . This book was released on 1995 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Asymptotic Behavior of the Term Structure of Interest Rates by : Maximilian Härtel
Download or read book The Asymptotic Behavior of the Term Structure of Interest Rates written by Maximilian Härtel and published by Cuvillier Verlag. This book was released on 2015-12-23 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long-term interest rates are essential for the valuation and hedging of various fixed income products and derivatives as well as for the pricing of payments in a distant future, such as long-term infrastructure projects or compensatory adjustments in the course of an accident or a divorce. In the aftermath of the 2008 financial crisis the modeling of interest rate curves with a long time horizon became more and more important due to increased investments in long-term products. Therefore, the study of the asymptotic behavior of the term structure of interest rates has recently achieved new relevance. In this dissertation we investigate long-term interest rates, i.e. interest rates with maturity going to infinity, in the post-crisis interest rate market. Three different concepts of long-term interest rates are considered for this purpose: the long-term yield, the long-term simple rate, and the long-term swap rate. We analyze the properties as well as the interrelations of these long-term interest rates. In particular, we study the asymptotic behavior of the term structure of interest rates in some specific models. First, we compute the three long-term interest rates in the HJM framework with different stochastic drivers, namely Brownian motions, Lévy processes, and affine processes on the state space of positive semidefinite symmetric matrices. The HJM setting presents the advantage that the entire yield curve can be modeled directly. Furthermore, by considering increasingly more general classes of drivers, we were able to take into account the impact of different risk factors and their dependence structure on the long end of the yield curve. Finally, we study the long-term interest rates and especially the long-term swap rate in the Flesaker-Hughston model and the linear-rational methodology. Langfristige Zinssätze werden für die Bewertung und Absicherung von festverzinslichen Finanzprodukten und Derivaten mit langer Laufzeit benötigt, sowie bei der Preisberechnung von Zahlungen, die in weiter Zukunft liegen. Solche Zahlungen kann es beispielsweise bei langfristig angelegten Infrastrukturprojekten geben oder bei Ausgleichsregelungen im Falle eines Unfalls oder einer Scheidung. Gerade im Zuge der weltweiten Finanzkrise von 2008 wuchs das Interesse von Anlegern an Investments mit langem Zeithorizont und damit auch die Notwendigkeit Zinskurven weiter in die Zukunft zu modellieren und das Verhalten am langen Ende der Kurven möglichst genau zu bestimmen. Die vorliegende Arbeit widmet sich der Untersuchung des asymptotischen Verhaltens von Zinskurven. Zu diesem Zwecke werden drei verschiedene langfristige Zinssätze analysiert: der langfristige stetige Zinssatz, der langfristige diskrete Zinssatz und der langfristige Swapzinssatz. Diese langfristigen Zinsen werden definiert als Zinssätze deren Laufzeit gegen unendlich geht im Rahmen eines Zinsmarktes, der auf Erkenntnissen basiert, die aus der Finanzkrise gewonnen werden konnten. Alle modellunabhängigen relevanten Eigenschaften dieser Zinsen werden erläutert und die Zusammenhänge zwischen ihnen werden genauestens hinsichtlich ihrer Wechselbeziehungen untersucht. Darüber hinaus ist ein wichtiger Teil dieser Dissertation der Beschreibung des asymptotischen Verhaltens von Zinskurven in speziellen Zinsmodellen gewidmet. Diese Modelle umfassen das Zinsstrukturmodell von Heath, Jarrow und Morton, genannt HJM Framework, das Flesaker-Hughston Modell sowie das linear-rationale Modell. Das HJM Framework wird aufgrund der Möglichkeit der direkten Modellierung der gesamten Zinsstrukturkurve und aller dazugehörigen Terminkurse für die Analyse verwendet. Die stochastische Komponente wird erst mittels der Brownschen Bewegung beschrieben, dann durch einen Lévy Prozess und zuletzt mit Hilfe eines affinen Prozesses auf dem Zustandsraum von positiv semidefiniten und symmetrischen Matrizen. Der Gebrauch dieser stochastischen Prozesse kann als schrittweise Weiterentwicklung des HJM Frameworks verstanden werden, da jeweils mehr, die Zinsstruktur beeinflussende, Faktoren in die Modellierung mit einfließen können. Die anderen beiden vorgestellten Modelle, das Flesaker-Hughston Modell und das linear-rationale Modell, finden, wegen einiger attraktiver Eigenschaften, Anwendung in der Analyse des asymptotischen Zinskurvenverhaltens, wie zum Beispiel einfache Formeln für alle Zinssätze, die keine negativen Werte annehmen können.
Book Synopsis The Term Structure of Interest Rates by : Marti G. Subrahmanyam
Download or read book The Term Structure of Interest Rates written by Marti G. Subrahmanyam and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most active areas of research in financial economics has been the modeling of the term structure of interest rates and its relationship to the pricing of contingent claims. There is a vast array of issues in the area, as well as a variety of perspectives, ranging from theoretical to practical. This paper provides a general framework for the analysis of issues in the modeling of the term structure. Specifically, this paper provides an overview of the conceptual issues and the empirical evidence in the area based on an examination of five seminal models by: Black-Scholes-Merton, Vasicek, Cox-Ingersoll-Ross, Ho- Lee and Heath-Jarrow-Morton. The paper provides a synthesis of the area and suggests directions for future research.
Book Synopsis Unspanned Stochastic Volatility Term Structure Model Applied in Negative Interest Rate Environment by : Jan Sedlak
Download or read book Unspanned Stochastic Volatility Term Structure Model Applied in Negative Interest Rate Environment written by Jan Sedlak and published by . This book was released on 2016 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest rate transition from the positive environment, into the negative territory questions the consensus of interest rates and opens up a wide field of unresearched areas. To cope with the changing interest rate environment as well as satisfying regulatory criteria, a model following the Heath-Jarrow-Morton framework with Unspanned Stochastic Volatility is implemented. The model is constructed to match shocks to the level, slope and curvature of the term structure. Estimation is performed with Libor rates, Government rates and Swaption ATM normal implied volatilities from 2006-01-01 to 2015-03-12. The model is backtested both in sample and out of sample and compared to a Normal model and a Log Normal model. The model shows a good quantile fit to the medium and long end of the term structure and performs relatively better then the two challenger models.
Book Synopsis Construction of a Single Factor Heath-Jarrow-Morton Term Structure Model by : Andrew Jeffrey
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:
Book Synopsis An Empirical Examination of Discrete Heath-Jarrow-Morton Term Structure Models by : David Thurston
Download or read book An Empirical Examination of Discrete Heath-Jarrow-Morton Term Structure Models written by David Thurston and published by . This book was released on 1993 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
