Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

by Renï Carmona, M R Tehranchi

Overview

Interest Rate Models: an Infinite Dimensional Shastic Analysis Perspective studies the mathematical issues that arise in modeling the interest rate term structure. These issues are approached by casting the interest rate models as shastic evolution equations in infinite dimensional function spaces. The book is comprised of three parts. Part I is a crash course on interest rates, including a statistical analysis of the data and an introduction to some popular interest rate models. Part II is a self-contained introduction to infinite dimensional shastic analysis, including SDE in Hilbert spaces and Malliavin calculus. Part III presents some recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.

Product Details

ISBN-13:	9783540270652
Publisher:	Springer Berlin Heidelberg
Publication date:	06/14/2006
Series:	Springer Finance
Edition description:	2006
Pages:	236
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

The Term Structure of Interest Rates.- Data and Instruments of the Term Structure of Interest Rates.- Term Structure Factor Models.- Infinite Dimensional Shastic Analysis.- Infinite Dimensional Integration Theory.- Shastic Analysis in Infinite Dimensions.- The Malliavin Calculus.- Generalized Models for the Term Structure of Interest Rates.- General Models.- Specific Models.

Editorial Reviews

From the reviews:

"Interest rate models … is a research monograph on the theory of interest rate models in infinite dimension. … Concepts are presented in detail with appropriate examples. … It is most suitable for researchers with good background in shastic and functional analysis … ." (Ita Cirovic Donev, MathDL-online, October, 2006)

"This book is a self-contained introduction to recent theoretical work that extends the Heath-Jarrow-Morton framework for modelling interest rates to infinite dimensions … . this is a wonderful book. The authors present some cutting-edge math in their extension of shastic calculus to infinite dimensions. … you will find this a fascinating read." (www.riskbook.com, August, 2006)

"This book gives a rigorous, fairly complete and remarkably clear introduction to the modelling of shastic term structure models from an infinite-dimensional point of view, and to recent research in that field. It can be used in multiple ways, as it can serve both as an introduction to the mechanics of interest rate modelling for specialists of shastic analysis, and as an introduction to infinite-dimensional analysis for mathematicians from other fields or for practitioners. Detailed bibliographic comments are included … ." (Nicolas Privault, Mathematical Reviews, Issue 2008 a)

From the Publisher