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# Lecture_00 - 0 PROLOGUE A The Approach This book studies a...

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1 0 P ROLOGUE A The Approach This book studies a new approach for understanding and analyzing fixed-income securities and interest rate options. It focuses on risk management, i.e., the arbitrage free pricing and hedging of fixed-income securities. This is in contrast to the traditional focus of textbooks in this area. Traditional textbooks

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2 This book provides a self-contained study of this new approach for pricing and hedging fixed-income securities and interest rate options. This new approach is called the Heath, Jarrow, and Morton (“HJM”) model. This approach is illustrated with the standard binomial model. The standard binomial model is chosen because of its mathematical simplicity. This is with little loss of generality, as the alternative and more complex stochastic calculus techniques need to be numerically implemented on a computer using the binomial model. With minor modifications, this technology can be easily extended (built upon) to handle the pricing of other more complex instruments, for example, foreign currency derivatives, commodity derivatives, and credit derivatives. B Motivation
3 Figure 1: Treasury Bond Yields on March 31, 1997 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0 5 10 15 20 25 30 Time (Years)

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4 A bond is an IOU issued for borrowing a stated amount of dollars (e.g. \$10,000), called the principal, for a period of time (e.g. 5 years), called the bond’s maturity. Interest is paid regularly (often semi-annually) on this IOU. A Treasury bond’s
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Lecture_00 - 0 PROLOGUE A The Approach This book studies a...

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