Chapter 31

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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