Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

Interest Rate Models: an Infinite Dimensional Stochastic 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 stochastic 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 stochastic 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.

• Infinite-Dimensional Stochastic Analysis
• Interest-Rate Models
• Malliavin Calculus
• calculus
• ergodicity
• modeling
• statistical analysis
• quantitative finance

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 stochastic 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 stochastic 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 stochastic 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 stochastic 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)

• Bendheim Center for Finance Department of Operations Research and Financial Engineering, Princeton University, Princeton, USA

  René A. Carmona

• Statistical Laboratory Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK

  Michael R. Tehranchi