Interest rate models: an infinite dimensional stochastic analysis perspective.

*(English)*Zbl 1124.91030
Springer Finance. Berlin: Springer (ISBN 3-540-27065-5/hbk). xiv, 235 p. (2006).

From the preface: “The level of complexity of the bond market is higher than for the equity markets…As a censequence, the mathematical model needed to describe their time evolution will have to be more involved. Indeed on each given day \(t\), instead of being given by a single number \(S_t\) as the price of one share of a common stock, the term structure of interest rates is given by a curve determined by a finite discrete set of values…

The main goal of the book is to present, in a self-contained manner, the empirical facts needed to understand the sophisticated mathematical models developed by the financial mathematics community over the last decade. So after a very elementary introduction to the mechanics of the bond market, and a thorough statistical analysis of the data available to any curious spectator without any special inside track information, we gradually introduce the mathematical tools needed to analyze the stochastic models most widely used in the industry.”

The book is divided into 3 parts:

I. The term structure of interest rates;

II. Infinite-dimensional stochastic analysis (infinite-dimensional integration theory, stochastic analysis in infinite dimensions, Malliavin calculus);

III. Generalised models for the term structure.

The reader of the book should have a solid background in probability theory, statistics and functional analysis.

The main goal of the book is to present, in a self-contained manner, the empirical facts needed to understand the sophisticated mathematical models developed by the financial mathematics community over the last decade. So after a very elementary introduction to the mechanics of the bond market, and a thorough statistical analysis of the data available to any curious spectator without any special inside track information, we gradually introduce the mathematical tools needed to analyze the stochastic models most widely used in the industry.”

The book is divided into 3 parts:

I. The term structure of interest rates;

II. Infinite-dimensional stochastic analysis (infinite-dimensional integration theory, stochastic analysis in infinite dimensions, Malliavin calculus);

III. Generalised models for the term structure.

The reader of the book should have a solid background in probability theory, statistics and functional analysis.

Reviewer: Peter Kischka (Jena)

##### MSC:

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

91G30 | Interest rates, asset pricing, etc. (stochastic models) |

60G44 | Martingales with continuous parameter |

60H07 | Stochastic calculus of variations and the Malliavin calculus |