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Quantitative Finance by Matt Davison

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Chapter 31

Interest Rate Models

31.1 CHAPTER SUMMARY

This chapter integrates the option pricing part of the book with the interest rate part of the book. The introductory Section 31.2 considers a bond to be a derivative on the spot interest rate, albeit a derivative for which the underlying cannot be hedged, a partial differential equation for the price of a zero coupon bond is developed. This requires some thinking about how to hedge when you cannot trade the underlying—this is done by hedging against another bond. A binomial tree model in Section 31.3 sets the stage for the resulting “market price of risk” discussion. With that in hand, a PDE can be developed for the price of a zero coupon bond, if the spot rate of interest follows a general ...

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