Download or read book Multi Factor Cox Ingersoll Ross Models of the Term Structure written by Ren-Raw Chen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a method for estimating multi-factor versions of the Cox, Ingersoll, Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility.

Download or read book The Valuation of Interest Rate Derivatives in a Multi Factor Term Structure Model with Deterministic Components written by Louis Scott and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the multi-factor Cox, Ingersoll, Ross (CIR) model of the term structure is extended by adding a deterministic component to the interest rate equation. This extra component makes the model flexible enough to match any initial term structure, while retaining the other features of the multi-factor CIR model. Current values for the random state variables can be set so that the model provides a good fit to the term structure, and the deterministic component can be used to fine tune the model for an exact fit. The model has nonnegative interest rates and relies on several random factors to capture the potential variability of the term structure, and it is easy to implement. In the paper, I present fast, closed form solutions for forward rates, futures rates, and several European interest rate options. Numerical methods for pricing other more complex interest rate derivatives are easy to implement because the model is Markovian; the distribution for interest rates each period depends on the current values for the state variables that determine the instantaneous interest rate. An important consequence of this feature is that nodes in a lattice model recombine. The paper also includes an application in which the model is calibrated to initial term structures in both the Treasury market and the Eurodollar futures market.

Download or read book Estimates of the Continuous Time Cox Ingersoll Ross Term Structure Model written by Purnendu Nath and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimates are made of multi-factor versions of the Cox-Ingersoll-Ross model of the term structure of interest rates using the Kalman filter. Estimates are obtained using weekly UK Gilt-edged market data over the period 1982-1997. Empirical results support the need for a multi-factor model and support recent findings of Babbs and Nowman for this market.

Download or read book On Term Structure of Yield Rates 2 The Cox Ingersoll Ross Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Interest Rate Options in Multifactor Cox Ingersoll Ross Models of the Term Structure written by Ren-Raw Chen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine valuation of interest rate options in multifactor versions of the Cox-Ingersoll-Ross model, including European options on discount bonds, European options on Eurodollar futures, and caps on floating interest rates. Valuation models for options on coupon bonds and coupon bond futures are also discussed. Standard solution techniques for such problems require numerical integration of a joint probability distribution, which becomes exceedingly time-consuming when there are more than two factors. We describe an alternative approach based on Fourier inversion methods that is much more efficient for solving multifactor models. In one example, using a three- factor model to price interest rate caps, our procedure reduces computation time from 2.83 hours to 1.93 seconds. Using this approach, we show that multifactor Cox-Ingersoll- Ross models generate prices for interest rate options that differ significantly from prices generated by Black's model when options with long-term expirations are valued. When a multifactor model is used for hedging, the hedge portfolio requires additional securities, and conventional formulas for hedge ratios must be modified.

Download or read book Interest Rate Term Structure Models written by Choongtze Chua and published by . This book was released on 2003 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Estimation of Term Structure Models and An Application to the United States written by International Monetary Fund and published by International Monetary Fund. This book was released on 2010-11-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses the estimation of models of the term structure of interest rates. After reviewing the term structure models, specifically the Nelson-Siegel Model and Affine Term- Structure Model, this paper estimates the terms structure of Treasury bond yields for the United States with pre-crisis data. This paper uses a software developed by Fund staff for this purpose. This software makes it possible to estimate the term structure using at least nine models, while opening up the possibility of generating simulated paths of the term structure.

Download or read book An Evaluation of Multi Factor Cir Models Using Libor Swap Rates and Cap and Swaption Prices written by Andrew Kaplin and published by . This book was released on 2010 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate the classical Cox, Ingersoll and Ross (1985) (CIR) model using data on LIBOR, swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. In particular the pricing errors are related to the slope of the swap yield curve. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid-ask spread in these markets. The model tends to overvalue shorter maturity caps and undervalue longer maturity caps. With only one or two factors, the model also tends to undervalue swaptions. Our findings point out the need for evaluating term structure models using data on derivative prices.

Download or read book An Assessment of Estimates of Term Structure Models for the United States written by Ying He and published by International Monetary Fund. This book was released on 2011-10-01 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper assesses estimates of term structure models for the United States. To this end, this paper first describes the mathematics underlying two types of term structure models, namely the Nelson-Siegel and Cox, Ingersoll and Ross family of models, and the estimation techniques. It then presents estimations of some of specific models within these families of models?three-factor Nelson-Siegel Model, four-factor Svensson model, and preference-free, two-factor Cox, Ingersoll and Roll model?for the United States from 1972 to mid 2011. It subsequently provides an assessment of the estimations. It concludes that these estimations of the term structure models successfully capture the dynamics of the term structure in the United States.

Download or read book Term Structure Modeling and Estimation in a State Space Framework written by Wolfgang Lemke and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been prepared during my work as a research assistant at the Institute for Statistics and Econometrics of the Economics Department at the University of Bielefeld, Germany. It was accepted as a Ph.D. thesis titled "Term Structure Modeling and Estimation in a State Space Framework" at the Department of Economics of the University of Bielefeld in November 2004. It is a pleasure for me to thank all those people who have been helpful in one way or another during the completion of this work. First of all, I would like to express my gratitude to my advisor Professor Joachim Frohn, not only for his guidance and advice throughout the com pletion of my thesis but also for letting me have four very enjoyable years teaching and researching at the Institute for Statistics and Econometrics. I am also grateful to my second advisor Professor Willi Semmler. The project I worked on in one of his seminars in 1999 can really be seen as a starting point for my research on state space models. I thank Professor Thomas Braun for joining the committee for my oral examination.

Download or read book Stochastic Calculus for Finance II written by Steven E. Shreve and published by Springer Science & Business Media. This book was released on 2004-06-03 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Download or read book The Term Structure of Interest Rates written by David Meiselman and published by . This book was released on 1962 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Interest Rate Models Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Testing Affine Yield Factor Models written by Jari Kappi and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article empirically tests single and multifactor versions of the Vasicek (1977) and Cox, Ingersoll, and Ross (1985) term structure models. These models belong to the class of affine term structure models proposed by Duffie and Kan (1996), where the affine relationship is between the yield of the discount bond and the abstract state variable. The maximum likelihood estimation method we apply allows us to utilize the conditional density of the state variables of the aforementioned models. The advantage of the estimation method is that we can recover the unobservable state variables from the yields of the discount bonds. Our results show that the single-factor models are unable to fit both the short and long ends of the yield curve simultaneously. The two-factor models miss the curvature of the yield curve, even though they can fit the level and the slope of the yield curve. A three-factor model is needed if we also want to capture the curvature of the yield curve. Moreover, the three-factor Vasicek model outperforms the three-factor CIR model.

Download or read book Mathematical Models in Finance written by S.D. Howison and published by CRC Press. This book was released on 1995-05-15 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models in Finance compiles papers presented at the Royal Society of London discussion meeting. Topics range from the foundations of classical theory to sophisticated, up-to-date mathematical modeling and analysis. In the wake of the increased level of mathematical awareness in the financial research community, attention has focused on fundamental issues of market modelling that are not adequately allowed for in the standard analyses. Examples include market anomalies and nonlinear coupling effects, and demand new synthesis of mathematical and numerical techniques. This line of inquiry is further stimulated by ever tightening profits due to increased competition. Several papers in this volume offer pointers to future developments in this area.

Download or read book Dynamic Term Structure Modeling written by Sanjay K. Nawalkha and published by John Wiley & Sons. This book was released on 2007-05-23 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Handbook of the Economics of Finance written by G. Constantinides and published by Elsevier. This book was released on 2003-11-04 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1B covers the economics of financial markets: the saving and investment decisions; the valuation of equities, derivatives, and fixed income securities; and market microstructure.