Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

This book probes mathematical issues that arise in modeling interest rate term structure, by casting the interest rate models as stochastic evolution equations in infinite dimensions. 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 recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.

Investigates interest rate models as stochastic evolution equations in infinite dimensions The three parts of the book offer an introduction to interest rates, a review of infinite dimensional stochastic analysis, and recent results in interest rate theory First book to combine infinite dimensional stochastic analysis with Malliavin calculus and interest rate market models Includes supplementary material: sn.pub/extras

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