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Nonparametric Pricing Of Interest Rate Derivative Securities
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Book Synopsis Nonparametric Pricing of Interest Rate Derivative Securities by : Yacine Ait-Sahalia
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Ait-Sahalia and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a nonparametric estimation procedure for continuous-time models and provides the asymptotic distribution of the estimator. Since the pricing of derivative securities depends crucially on the form of the instantaneous volatility of the underlying asset, the diffusion function of the spot interest rate is unrestricted and estimated nonparametrically. The diffusion function is identified by requiring that the distribution of the process match that of the data. Even though only discrete data are used, the estimation procedure does not rely on replacing the continuous-time process by some discrete approximation. The continuous-time process followed by the short term interest rate is estimated. Nonparametric prices are computed for bonds, yielding the term structure of interest rates, and bond options.
Book Synopsis Nonparametric Pricing of Interest Rate Derivative Securities by : Yacine Aït-Sahalia
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Aït-Sahalia and published by . This book was released on 1995 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a nonparametric estimation procedure for continuous- time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous- time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options.
Book Synopsis Nonparametric Pricing of Interest Rate Derivative Securities by : Yacine Ai t-Sahalia
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Ai t-Sahalia and published by . This book was released on 1993 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing Interest Rate Derivatives in a Non-Parametric Two-Factor Term-Structure Model by : John Knight
Download or read book Pricing Interest Rate Derivatives in a Non-Parametric Two-Factor Term-Structure Model written by John Knight and published by . This book was released on 2000 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion functions in term-structure models are measures of uncertainty about future price movements and are directly related to the risk associated with holding financial securities. Correct specification of diffusion functions is crucial in pricing options and other derivative securities. In contrast to the standard parametric two-factor models, we propose a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions. Hence, this model allows for maximum flexibility when fitting diffusion functions into data. A non-parametric procedure is developed for estimating the diffusion functions, based on the discretely sampled observations. The convergence properties and the asymptotic distributions of the proposed non-parametric estimators of the diffusion functions with multivariate dimensions are also obtained. Based on U.S. data, the non-parametric prices of the bonds and bond options are computed and compared with those calculated under an alternative parametric model. The empirical results show that the non-parametric model generates significantly different prices for the derivative securities.
Book Synopsis The Valuation of Interest Rate Derivative Securities by : Jeroen F. J. De Munnik
Download or read book The Valuation of Interest Rate Derivative Securities written by Jeroen F. J. De Munnik and published by Routledge. This book was released on 2005-10-18 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increased volatility of interest rates during recent years and the corresponding introduction of a variety of interest rate derivative securities like bond options, futures and embedded options in mortgages, underlines the need for a comprehensive financial theory to determine values of fixed income instruments and derivative securities consistently. This book provides: * a detailed overview and classification of the different approaches to value interest rate dependent securities * a comparison of the numerical approaches to value complex securities * an empirical examination for the Dutch Fixed Income Market of some well-known interest rate models which demonstrates recent improvements to describe interest rate movements in relation to contingent claim valuation.
Book Synopsis A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk by : Richard Stanton
Download or read book A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk written by Richard Stanton and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper nonparametrically estimates a continuous-time Markov model of term structure dynamics. Due to the quot;aliasing problemquot;, which tells us that the drift and diffusion of the short rate process are not identifiable given only discretely sampled data, previous authors have parameterized at least one of the drift and diffusion functions, leaving open the possibility of misspecification. This paper imposes no parametric restrictions on either the drift or the diffusion, instead deriving and estimating a family of approximations to the true drift and diffusion functions. These approximations are identifiable using only discretely observed data, and for some common parametric models, we find that the approximations are almost indistinguishable from the true drift and diffusion when the sampling frequency is monthly or greater. Estimating the model using daily data on the 3 month Treasury Bill rate over the period January 1965 - July 1995, we find that, while the estimated diffusion is similar to the (parametric) function estimated by Chan, Karolyi, Longstaff and Sanders (1992), there is evidence of substantial nonlinearity in the drift, showing sharply increasing mean reversion as the short rate moves further from its long run mean. Knowing the process governing short term interest rate movements is not enough by itself to price interest rate derivative securities. We also need to know the market price of interest rate risk, the excess return required for an investor to bear a unit amount of additional risk. Previous research has typically assumed this to be identically zero. We explicitly estimate the functional relationship between the market price of interest rate risk and the level of interest rates, using daily excess returns on 6 month vs. 3 month Treasury Bills over the period January 1965 - July 1995, and combine this with the estimated short rate model to price interest rate dependent securities. Incorporating our estimates for the market price of interest rate risk changes the pricing results substantially.
Book Synopsis Efficient Methods for Valuing Interest Rate Derivatives by : Antoon Pelsser
Download or read book Efficient Methods for Valuing Interest Rate Derivatives written by Antoon Pelsser and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues.
Book Synopsis Pricing Derivative Securities (2nd Edition) by : Thomas Wake Epps
Download or read book Pricing Derivative Securities (2nd Edition) written by Thomas Wake Epps and published by World Scientific Publishing Company. This book was released on 2007-06-04 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also covers pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes. Readers begin with simple, discrete-time models that require little mathematical sophistication, proceed to the basic Black-Scholes theory, and then advance to continuous-time models with multiple risk sources. The second edition takes account of the major developments in the field since 2000. New topics include the use of simulation to price American-style derivatives, a new one-step approach to pricing options by inverting characteristic functions, and models that allow jumps in volatility and Markov-driven changes in regime. The new chapter on interest-rate derivatives includes extensive coverage of the LIBOR market model and an introduction to the modeling of credit risk. As a supplement to the text, the book contains an accompanying CD-ROM with user-friendly FORTRAN, C++, and VBA program components.
Book Synopsis Fixed Income and Interest Rate Derivative Analysis by : Mark Britten-Jones
Download or read book Fixed Income and Interest Rate Derivative Analysis written by Mark Britten-Jones and published by Elsevier. This book was released on 1998-10-15 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Income and Interest Rate Derivative Analysis gives a clear and accessible approach to the analytical techniques of debt instrument valuation. Without using complicated mathematical abstractions, this text shows that the fundamentals of fixed income and interest rate derivate analysis can be easily understood when seen as a small number of simple economic concepts. Concepts inroduced in this book are reinforced and explained, not with the use of high-powered mathematics, but with actual examples of various market instruments and case studies from North America, Europe, Australia and Hong Kong. The text also contains review questions which aid the reader in their understanding. Mark Britten-Jones, BEcon, MA, PhD, is an Assistant Professor of Finance at the London Business School where he teaches Fixed Income Securities and Markets as part of a MBA and Master's course in Finance. A comprehensive and accessible explanation of underlying theory, and its practical application Case studies and worked examples from around the world's capital markets How to use spreadsheet modelling in fixed income and interest rate derivative valuation
Book Synopsis The Pricing of Interest Rate Derivative Securities by : Stefan Glunz
Download or read book The Pricing of Interest Rate Derivative Securities written by Stefan Glunz and published by . This book was released on 1997 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) by : Nicolas Privault
Download or read book Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) written by Nicolas Privault and published by World Scientific. This book was released on 2021-09-02 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.
Book Synopsis Nonparametric Econometric Methods by : Qi Li
Download or read book Nonparametric Econometric Methods written by Qi Li and published by Emerald Group Publishing. This book was released on 2009-12-04 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.
Book Synopsis Pricing Interest Rate Derivatives by : George Chacko
Download or read book Pricing Interest Rate Derivatives written by George Chacko and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between affine stochastic processes and bong pricing equations in exponential term structure models has been well established. We connect this result to the pricing of interest rate derivatives. If the term structure model is exponential afffine, then there is a linkage between the bond pricing solution and the prices of many widely traded interest rate derivative securities. Our results apply to m-factor processes with n diffusions and l jump processes. The pricing solutions require at most a single numerical integral, making the model easy to implement. We discuss many options that yield solutions using the methods of the article.
Book Synopsis Valuation and Risk Management of Interest Rate Derivative Securities by : Stephan Leithner
Download or read book Valuation and Risk Management of Interest Rate Derivative Securities written by Stephan Leithner and published by . This book was released on 1992 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Interest Rate Dynamics, Derivatives Pricing, and Risk Management by : Lin Chen
Download or read book Interest Rate Dynamics, Derivatives Pricing, and Risk Management written by Lin Chen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A New Approach to the Valuation of Interest Rate Derivatives by : Padideh Jalali
Download or read book A New Approach to the Valuation of Interest Rate Derivatives written by Padideh Jalali and published by . This book was released on 1999 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a complete, arbitrage-free securities market, the value of a discount bond is modeled in terms of the pricing kernel and the transition density function of the spot interest rate process. The prices of discount bonds are taken from the current term structure of interest rates, and the transition density function is estimated from historical term structure data, using both parametric and nonparametric techniques. The pricing kernel and associated prices of Arrow-Debreu securities are then determined. The resulting Arrow-Debreu prices have two merits: they are consistent with the current term structure of interest rates, and therefore arbitrage-free, and, in addition, they embody the observed historical behavior of the term structure.
Book Synopsis PDE Valuation of Interest Rate Derivatives by : Peter Kohl-Landgraf
Download or read book PDE Valuation of Interest Rate Derivatives written by Peter Kohl-Landgraf and published by BoD – Books on Demand. This book was released on 2007 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Libor Market Model and its several extensions can be seen as state of the art in interest rate modeling. However, due to the ever increasing complexity of interest rate products, the high dimensionality of this approach starts to reach its limits from the computational side. This book is mainly concerned with a class of Markovian Yield Curve Models which try to overcome that disadvantage as they enable a low-dimensional deterministic and fast PDE valuation. The objective of this book is thereby threefold: - To illuminate in a compact way the connection between stochastic processes and partial differential equations as well as review the key features of arbitrage-free pricing. - To embed the here analyzed Markovian model class into the entire framework of interest rate models. - To present and implement robust numerical schemes, which enable an efficient computational treatment of risk-neutral product valuation by using PDE methods.
