AN ELEMENTARY INTRODUCTION TO STOCHASTIC INTEREST RATE MODELING (Advanced Series on Statistical Science and Applied Probability)

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This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students. Contents: A Review of Stochastic Calculus; A Review of Black Scholes Pricing; Short Term Interest Rate Models; Pricing of Zero-Coupon Bonds; Forward Rate Modeling; The Heath Jarrow Morton (HJM) Model; The Forward Measure and Derivative Pricing; Curve Fitting and a Two-Factor Model; Pricing of Caps and Swaptions on the LIBOR; The Brace Gatarek Musiela (BGM) Model; Mathematical Tools; Some Recent Developments; Solutions to the Exercises.