An Elementary Introduction to Stochastic Interest Rate Modeling

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World Scientific, 2008 - Science - 178 pages
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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.
 

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Contents

A Review of Stochastic Calculus
1
A Review of BlackScholes Pricing
13
Short Term Interest Rate Models
29
Forward Rate Modeling
47
The HeathJarrowMorton HJM Model
57
The Forward Measure and Derivative Pricing
73
Curve Fitting and a Two Factor Model
85
Pricing of Caps and Swaptions on the LIBOR
103
The BraceGatarekMusiela BGM Model
121
Mathematical Tools
135
Some Recent Developments
143
Bibliography
173
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