On Term Structure of Yield Rates. 2. The Cox - Ingersoll - Ross Model PDF Download
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Author: Gennady Medvedev Publisher: ISBN: Category : Languages : en Pages : 7
Book Description
Historically, the first popular model of the dynamics of the interest rate is the Vasiček model proposed in 1977. It was considered in the preceding article. In this model, the interest rate has a normal distribution, which is obviously economically untenable, because in terms of the interest rate can not take negative values. At the same time, this model has been used by many for the reason that in many cases the ratio between the average and variance of real rates is such that the probability of their negative values appears very small. At the same time, the analysis of Vasicek's model and the prices of assets based on it is very simple, since it leads to linear problems. Later in 1985, Cox, Ingersoll and Ross proposed another model, also called a "square root model," under which the interest rate assumes only non-negative values and has a gamma distribution. Analysis of interest rates and asset prices based on this model also allows for analytical results, but they are significantly more difficult, since they suggest solving non-linear problems. The possibility of obtaining analytical results is the main advantage of affine models. Analytical results are important, because otherwise yields should be calculated either by Monte Carlo methods or by methods of solving partial differential equations. Both of these approaches are computationally time-consuming, especially when model parameters need to be estimated using samples from bond yield data. Therefore, the literature on determining the bond prices, starting with the works of Vasiček and Cox, Ingersoll and Ross, focused on solutions in a closed form. From a practical point of view it is interesting to consider the problem of how much the results obtained with the help of these models differ. The main purpose of this article is to obtain analytical solutions when analyzing the time structure of interest rates for the yield of zero-coupon bonds using the Cox-Ingersoll-Ross model in a single-factor and multifactor variants. It also compares the yield curves and forward curves resulting from the short-term interest rate behavior models mentioned above.
Author: Gennady Medvedev Publisher: ISBN: Category : Languages : en Pages : 7
Book Description
Historically, the first popular model of the dynamics of the interest rate is the Vasiček model proposed in 1977. It was considered in the preceding article. In this model, the interest rate has a normal distribution, which is obviously economically untenable, because in terms of the interest rate can not take negative values. At the same time, this model has been used by many for the reason that in many cases the ratio between the average and variance of real rates is such that the probability of their negative values appears very small. At the same time, the analysis of Vasicek's model and the prices of assets based on it is very simple, since it leads to linear problems. Later in 1985, Cox, Ingersoll and Ross proposed another model, also called a "square root model," under which the interest rate assumes only non-negative values and has a gamma distribution. Analysis of interest rates and asset prices based on this model also allows for analytical results, but they are significantly more difficult, since they suggest solving non-linear problems. The possibility of obtaining analytical results is the main advantage of affine models. Analytical results are important, because otherwise yields should be calculated either by Monte Carlo methods or by methods of solving partial differential equations. Both of these approaches are computationally time-consuming, especially when model parameters need to be estimated using samples from bond yield data. Therefore, the literature on determining the bond prices, starting with the works of Vasiček and Cox, Ingersoll and Ross, focused on solutions in a closed form. From a practical point of view it is interesting to consider the problem of how much the results obtained with the help of these models differ. The main purpose of this article is to obtain analytical solutions when analyzing the time structure of interest rates for the yield of zero-coupon bonds using the Cox-Ingersoll-Ross model in a single-factor and multifactor variants. It also compares the yield curves and forward curves resulting from the short-term interest rate behavior models mentioned above.
Author: Rajna Gibson Publisher: Now Publishers Inc ISBN: 1601983727 Category : Business & Economics Languages : en Pages : 171
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: Emilio Barone Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
This paper tests the Cox, Ingersoll and Ross model using the prices of Italian Treasury bonds in the secondary market. The model is estimated daily for the period 30 December 1983 to 13 March 1989. The resulting term structures of interest rates are compared with those obtained using interpolation techniques (the cubic splines method). The daily estimation of the yield curves also makes it possible to analyze the changes in Treasury bond prices, determine the turning points and obtain useful indications regarding the efficiency of the secondary market and the consistency between the primary and the secondary markets.
Author: Damiano Brigo Publisher: Springer Science & Business Media ISBN: 354034604X Category : Mathematics Languages : en Pages : 1016
Book Description
The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
Author: Burton Gordon Malkiel Publisher: Princeton University Press ISBN: 1400879787 Category : Business & Economics Languages : en Pages : 294
Book Description
Can expectations alone explain the yield differentials among bonds of different maturities? To what extend do attitudes toward risk and transactions costs influence the behavior of bond investors? Is it possible for the Federal Reserve to "twist" the interest-rate structure in accordance with its policy objectives? These are among the questions treated. Originally published in 1966. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Frank J. Fabozzi Publisher: John Wiley & Sons ISBN: 047144698X Category : Business & Economics Languages : en Pages : 530
Book Description
This ultimate guide contains an excellent blend of theory and practice This comprehensive guide covers various aspects of model building for fixed income securities and derivatives. Filled with expert advice, valuable insights, and advanced modeling techniques, Interest Rate, Term Structure, and Valuation Modeling is a book that all institutional investors, portfolio managers, and risk professionals should have. John Wiley & Sons, Inc. is proud to be the publisher of the esteemed Frank J. Fabozzi Series. Comprising nearly 100 titles-which include numerous bestsellers—The Frank J. Fabozzi Series is a key resource for finance professionals and academics, strategists and students, and investors. The series is overseen by its eponymous editor, whose expert instruction and presentation of new ideas have been at the forefront of financial publishing for over twenty years. His successful career has provided him with the knowledge, insight, and advice that has led to this comprehensive series. Frank J. Fabozzi, PhD, CFA, CPA, is Editor of the Journal of Portfolio Management, which is read by thousands of institutional investors, as well as editor or author of over 100 books on finance for the professional and academic markets. Currently, Dr. Fabozzi is an adjunct Professor of Finance at Yale University's School of Management and on the board of directors of the Guardian Life family of funds and the Black Rock complex of funds.
Author: Javier F. Navas Publisher: ISBN: Category : Languages : en Pages : 36
Book Description
We study the fitting of the euro yield curve with the Longstaff and Schwartz (1992) (LS) two - factor general equilibrium model and the Schaefer and Schwartz (1984) (SS) two-factor arbitrage model of the term structure of interest rates. The Cox, Ingersoll, and Ross (1985b) (CIR) one-factor model is also studied as a reference. LS use the short - term interest rate and the volatility of the short-term interest rate as state variables, while SS use the spread between the short-term and the long - term interest rate and the long-term interest rate. Thus, the LS model should perform better (worse) than the SS model in pricing short-term (long - term) securities. Moreover, since the CIR model can be nested into the LS model, we expect the latter model to perform better than the former.The results show that, as expected, the LS model is best adjusting to the short - term yields. Surprisingly, the CIR model is best fitting to long - term yields. In any case, the three models have difficulties matching both the entire yield curve and the term structure of volatilities.
Author: Gennady Medvedev
Author: Gennady Medvedev
Author: David Meiselman
Author: Roger H. Brown
Author: Rajna Gibson
Author: Neil D. Pearson
Author: Emilio Barone
Author: Damiano Brigo
Author: Burton Gordon Malkiel
Author: Frank J. Fabozzi
Author: Javier F. Navas