Yield Curves and Forward Curves for Diffusion Models of Short Rates
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,
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Yield Curves and Forward Curves for Diffusion Models of Short Rates
Yield Curves and Forward Curves for Diffusion Models of Short Rates
Gennady A. Medvedev
Yield Curves and Forward Curves for Diffusion Models of Short Rates
123
Gennady A. Medvedev Belarusian State University Minsk, Belarus
ISBN 978-3-030-15499-8 ISBN 978-3-030-15500-1 https://doi.org/10.1007/978-3-030-15500-1
(eBook)
Library of Congress Control Number: 2019935988 Mathematics Subject Classification (2010): 91G80, 91G70 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Interest in studying the term structure of interest rates grew significantly after the appearance in 1977 of a famous article by the Czech mathematician Oldřich Vašíček, in which he gave a clear mathematical outline of the procedure for determining the general form of the term structure, derived the term structure equation, and demonstrated its solution in the case when the random process of the short-term rate is an Ornstein–Uhlenbeck diffusion process. Subsequently, this case became known as the Vasiček model of short-term interest rates. We note that the term structure equation was derived by Vasiček from the requirement of the absence of arbitrage opportunities in the financial market. We denote by P(r, t, T) the price at time t of the discount bond maturing at time T; t T, with unit maturity value P(r, T, T) = 1. Here, r = r(t) is a short-term rate (an instantaneous borrowing and lending interest rate) at time t. The price P(r, t, T) may be written as Pðr; t; t þ sÞ, where s ¼ T t is the term to maturity. Then, Pðr; t; t þ sÞ, considered as a function of s, will be referred to as the term structure at ti
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