Term Structure Models With Parallel And Proportional Shifts
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Term Structure Models with Parallel and Proportional Shifts
We investigate the possibility of an arbitrage free model for the term structure of interest rates where the yield curve only changes through a parallel shift. We consider HJM type forward rate models driven by a multidimensionalWiener process as well as by a general marked point process. Within this general framework we show that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. We also show that there exists no nontrivial flat term structure model. The same analysis is repeated for the similar case, where the yield curve only changes through proportional shifts. Key words: bond market, term structure of interest rates, flat term structures.
Term-Structure Models
Author: Damir Filipovic
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-07-28
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
Pricing and Hedging Interest and Credit Risk Sensitive Instruments
This book is tightly focused on the pricing and hedging of fixed income securities and their derivatives. It is targeted at those who are interested in trading these instruments in an investment bank, but is also useful for those responsible for monitoring compliance of the traders such as regulators, back office staff, middle and senior lever managers. To broaden its appeal, this book lowers the barriers to learning by keeping math to a minimum and by illustrating concepts through detailed numerical examples using Excel workbooks/spreadsheets on a CD with the book. On the accompanying CD with the book, three interest rate models are illustrated: Ho and Lee, constant volatility and Black Derman and Toy, along with two evolutionary models, Vasicek and CIR and two credit risk models, Jarrow and Turnbull and Duffie and Singleton. These are implemented via spreadsheets on the CD.* Starts at an introductory level and then develops advanced topics * Provides plenty of numerical examples rather than mathematical equations to aid full understanding of the strengths and weaknesses of all interest rate derivative models* Can be used for self-study - a complete book on the topic, which includes examples with answers