The LIBOR Market Model in Practice [Hardcover]

This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.

Acknowledgments ix

About the Authors xi

Introduction xiii

Part I THEORY 1

1 Mathematics in a Pill 3

1.1 Probability Space and Random Variables 3

1.2 Normal Distributions 4

1.3 Stochastic Processes 4

1.4 Wiener Processes 5

1.5 Geometric Wiener Processes 5

1.6 Markov Processes 6

1.7 Stochastic Integrals and Stochastic Differential Equations 6

1.8 Ito’s Formula 7

1.9 Martingales 7

1.10 Girsanov’s Theorem 7

1.11 Black’s Formula (1976) 8

1.12 Pricing Derivatives and Changing of Numeraire 8

1.13 Pricing of Interest Ratelë