An elementary introduction to stochastic interest rate modeling.
2nd ed.

*(English)*Zbl 1248.91002
Advanced Series on Statistical Science & Applied Probability 16. Hackensack, NJ: World Scientific (ISBN 978-981-4390-85-9/hbk; 978-981-4390-86-6/ebook). xiii, 228 p. (2012).

The book is devoted to stochastic interest rate models from short rate to forward rate models such as the Heath-Jarrow-Morton and Brace-Gatarek-Musiela models, for which an introduction to calibration is given. The focus is placed on a step by step introduction of concepts and explicit calculations, in particular for the pricing of associated derivatives such as caps and swaptions. The first two chapters are devoted to reviews of stochastic calculus and classical Black-Scholes procing for options on equities. Next, after a rapid representation of short term interest rate models in Chapter 3, the author turns to the definition and pricing of zero-coupon bonds in Chapter 4. Forward rates, instantaneous rates and their modeling using function spaces are considered in Chapter 5. The stochastic Heath-Jarrow-Morton model for the modeling of forward rates is described in Chapter 6. Chapter 7 contains the construction of forward measures and its consequences on the pricing of interest rate derivatives. Chapter 8 is devoted to the problem of estimation and fitting of interest rate curves. Chapter 9 describes a credit default model, in Chapter 9 pricing of caps and swaptions is studied, and Chapter 11 is devoted to Brace-Gatarek-Musiela model. The book is aimed at the advanced undergraduate and beginning graduate levels, assuming that the reader knows the basics of probability and stochastic calculus.

Reviewer: Yuliya S. Mishura (Kyïv)

##### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91B24 | Microeconomic theory (price theory and economic markets) |

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

60H05 | Stochastic integrals |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |