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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: 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: 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: Gennady A. Medvedev Publisher: Springer ISBN: 3030155005 Category : Mathematics Languages : en Pages : 230
Book Description
This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.
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: 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: Moorad Choudhry Publisher: John Wiley & Sons ISBN: 1119141060 Category : Business & Economics Languages : en Pages : 384
Book Description
Understand and interpret the global debt capital markets Now in a completely updated and expanded edition, this is a technical guide to the yield curve, a key indicator of the global capital markets and the understanding and accurate prediction of which is critical to all market participants. Being able to accurately and timely predict the shape and direction of the curve permits practitioners to consistently outperform the market. Analysing and Interpreting the Yield Curve, 2nd Edition describes what the yield curve is, explains what it tells participants, outlines the significance of certain shapes that the curve assumes and, most importantly, demonstrates what factors drive it and how it is modelled and used. Covers the FTP curve, the multi-currency curve, CSA, OIS-Libor and 3-curve models Gets you up to speed on the secured curve Describes application of theoretical versus market curve relative value trading Explains the concept of the risk-free rate Accessible demonstration of curve interpolation best-practice using cubic spline, Nelson-Siegel and Svensson 94 models This advanced text is essential reading for traders, asset managers, bankers and financial analysts, as well as graduate students in banking and finance.
Author: Gennady Medvedev
Author: Gennady Medvedev
Author: Roger H. Brown
Author: David Meiselman
Author: Neil D. Pearson
Author: Emilio Barone
Author: Rajna Gibson
Author: Gennady A. Medvedev
Author: Javier F. Navas
Author: Burton Gordon Malkiel
Author: Moorad Choudhry