Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

✍ Scribed by René A. Carmona, Michael R. Tehranchi (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2006
• Tongue: English
• Leaves: 239
• Series: Springer Finance
• Edition: 1
• Category: Library

✦ Synopsis

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 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 some recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.

✦ Table of Contents

Front Matter....Pages 1-1
Data and Instruments of the Term Structure of Interest Rates....Pages 3-42
Term Structure Factor Models....Pages 43-72
Front Matter....Pages 73-73
Infinite Dimensional Integration Theory....Pages 75-100
Stochastic Analysis in Infinite Dimensions....Pages 101-133
The Malliavin Calculus....Pages 135-159
Front Matter....Pages 161-161
General Models....Pages 163-194
Specific Models....Pages 195-215

✦ Subjects

Quantitative Finance; Financial Economics