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Author: Kristian R. Miltersen Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts.Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.
Author: Kristian R. Miltersen Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts.Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.
Author: Richard C. Stapleton Publisher: ISBN: Category : Interest rate futures Languages : en Pages : 65
Book Description
We derive general properties of two-factor models of the term structure of interest rates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. In this model, the term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional, autoregressive process for the short-term rate, which exhibits both mean-reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatilities and the correlations of the futures rates of various maturities. These are shown to be related to the volatility of the short rate, the volatility of the second factor, the degree of mean-reversion and the persistence of the second factor shock. We also discuss the extension of our model to three or more factors. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate LIBOR follows a two-dimensional process. Our results lead to empirical hypotheses that are testable using data from the liquid market for Eurocurrency interest rate futures contracts.
Author: T.S. Ho Publisher: ISBN: Category : Languages : en Pages : 39
Book Description
We derive a no-arbitrage model of the term structure in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional ARMA process for the short rate which exhibits mean reversion and a lagged memory parameter. We show that the correlation of the factor rates is restricted by the no-arbitrage conditions of the model. Hence in a multiple-factor model it is not valid to independently choose both the mean reversion, volatility and correlation parameters. The term-structure model, derived here, can be used to value options on bonds and swaps or to generate term structure scenarios for the risk management of portfolios of interest-rate derivatives.
Author: Richard C. Stapleton Publisher: ISBN: Category : Languages : en Pages : 51
Book Description
We derive general properties of two-factor models of the term structure of interest rates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional autoregressive process for the short-term rate, which exhibits both mean reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatility of the futures rates of various maturities. These are shown to be related to the volatilities of the short rate, the volatility of the second factor, the degree of mean reversion and the persistence of the second factor shock. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate (Libor)] follows a two-dimensional process. Our results lead to empirical hypotheses that are testable using data from the liquid market for Eurocurrency interest rate futures contracts.
Author: Eliezer Z Prisman Publisher: World Scientific ISBN: 9813149787 Category : Business & Economics Languages : en Pages : 269
Book Description
Written for undergraduates, this book is dedicated to fixed income fundamentals that do not require modeling the dynamics of interest rates. The book concentrates on understanding and explaining the pillars of fixed income markets, using the modern finance approach implied by the 'no free lunch' condition. It focuses on conceptual understanding so that novice readers will be familiar with tools needed to analyze bond markets. Institutional information is covered only to the extent that is necessary to obtain full appreciation of concepts.This volume will equip readers with a solid and intuitive understanding of the No Arbitrage Condition — its link to the existence and estimation of the term structure of interest rates, and to valuation of financial contracts. Using the modern approach of arbitrage arguments, the book addresses positions and contracts that do not require modeling evolution of interest rates. As such, it welcomes readers lacking the technical background for this modeling, and provides them with good intuition for interest rates, no arbitrage condition, bond markets and certain financial contracts.
Author: Sandra Peterson Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
We build a no-arbitrage model of the term structure of interest rates using two stochastic factors, the short-term interest rate and the premium of the futures rate over the short-term interest rate. The model provides and extension of the lognormal interest rate model of Black and Karasinski (1991) to two factors, both of which can exhibit mean-reversion. The method is computationally efficient for several reasons. First, the model is based on Libor futures prices, enabling us to satisfy the no-arbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multiperiod tree of rates with the no-arbitrage property. The method uses a recombining two-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and floors. These prices are shown to be highly sensitive to the existence of the second factor and its volatility characteristics.
Author: Sanjay K. Nawalkha Publisher: John Wiley & Sons ISBN: 0470140062 Category : Business & Economics Languages : en Pages : 722
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: Robert Brooks Publisher: Wiley ISBN: 9780943205380 Category : Business & Economics Languages : en Pages : 40
Book Description
This monograph addresses the return side of the decision to use interest rate swaps or other interest-rate-contingent claims. Because the economic costs of decisions related to a company's policies toward debt maturities are important to stock price performance, the analysis in this monograph has practical implications for investment analysts. Brooks demonstrates how an at-the-market swap with a risk premium can have a significant impact on the expected return from using the swap.
Author: Kristian R. Miltersen
Author: Kristian R. Miltersen
Author: Richard C. Stapleton
Author: T.S. Ho
Author: Richard C. Stapleton
Author: Eliezer Z Prisman
Author: Sandra Peterson
Author: Sandra Peterson
Author: Sanjay K. Nawalkha
Author: Thomas Gustavsson
Author: Robert Brooks