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Author: Richard Stanton
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Richard Stanton
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Rajna Gibson
Publisher: Now Publishers Inc
ISBN: 1601983727
Category : Business & Economics
Languages : en
Pages : 171
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Book Description
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: John L. Knight
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 60
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Book Description
Proposes a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions.
Author: Takashi Yasuoka
Publisher: Bentham Science Publishers
ISBN: 1681086891
Category : Business & Economics
Languages : en
Pages : 325
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Book Description
Interest Rate Modeling for Risk Management presents an economic model which can be used to compare interest rate and perform market risk assessment analyses. The key interest rate model applied in this book is specified under real-world measures, and the result is used as to generate scenarios for interest rates. The book introduces a theoretical framework that allows estimating the market price of interest rate risk. For this, the book starts with a brief explanation of stochastic analysis, and introduces interest rate models such as Heath-Jarrow-Morton, Hull-White and LIBOR models. The real-world model is then introduced in subsequent chapters. 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 of risk (with practical examples). 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. The second edition features an expanded commentary on real world models as well as additional numerical examples for the benefit of readers.
Author: Antonio Mele
Publisher: MIT Press
ISBN: 0262046849
Category : Business & Economics
Languages : en
Pages : 1147
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Book Description
A comprehensive reference for financial economics, balancing theoretical explanations, empirical evidence, and the practical relevance of knowledge in the field. This volume offers a comprehensive, integrated treatment of financial economics, tracking the major milestones in the field and providing methodological tools. Doing so, it balances theoretical explanations, empirical evidence, and practical relevance. It illustrates nearly a century of theoretical advances with a vast array of models, showing how real phenomena (and, at times, market practice) have helped economists reformulate existing theories. Throughout, the book offers examples and solved problems that help readers understand the main lessons conveyed by the models analyzed. The book provides a unique and authoritative reference for the field of financial economics. Part I offers the foundations of the field, introducing asset evaluation, information problems in asset markets and corporate finance, and methods of statistical inference. Part II explains the main empirical facts and the challenges these pose for financial economists, which include excess price volatility, market liquidity, market dysfunctionalities, and the countercyclical behavior of market volatility. Part III covers the main instruments that protect institutions against the volatilities and uncertainties of capital markets described in part II. Doing so, it relies on models that have become the market standard, and incorporates practices that emerged from the 2007–2008 financial crisis.
Author: John Knight
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Book Description
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.
Author: Dong-Hyun Ahn
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Recent nonparametric estimation studies pioneered by Ait-Sahalia (1996a, 1996b) document that the diffusion of the short rate is similar to the parametric function, r1.5, estimated by Chan, Karolyi, Longstaff, and Sanders (1992) whereas the drift is substantially nonlinear in the short rate. These empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior. This paper presents such a model. Our model delivers closed-form solutions for bond prices and concave relationship between the interest rate and the yields. We show that in empirical analyses, our model outperforms the one-factor affine models in both time-series as well as cross-sectional tests.
Author: Cornelis Los
Publisher: Routledge
ISBN: 1134469322
Category : Business & Economics
Languages : en
Pages : 483
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Book Description
This book covers the latest theories and empirical findings of financial risk, its measurement and management, and its applications in the world of finance.
Author: Sanjay K. Nawalkha
Publisher: John Wiley & Sons
ISBN: 0470140062
Category : Business & Economics
Languages : en
Pages : 722
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Book Description
Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling
Author: Qi Li
Publisher: Princeton University Press
ISBN: 0691121613
Category : Business & Economics
Languages : en
Pages : 768
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Book Description
This is a graduate textbook for econometricians and statisticians containing developments in the field. It emphasises nonparametric methods for real world problems containing the mix of discrete and continuous data found in many applications.
