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section7 (1) - Continuous Time Finance Notes Spring 2004...

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Continuous Time Finance Notes, Spring 2004 – Section 7, March 10, 2004 Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use in connec- tion with the NYU course Continuous Time Finance. Brief announcements concerning the rest of this semester: HW 4 will be available after spring break, and will be due March 31. HW5 will be due April 14. HW6 will be due April 28. The final exam will be in the normal class slot on May 5. You may bring two sheets of your own notes (both sides of each page, any font) to the exam, but you may not use books, my notes, HW solutions, etc. ***************** The March 10 lecture covered one-factor HJM, following closely the treatment in Baxter and Rennie. So I’ll just outline what was done in class; please read the book for details. The essential concept of HJM is to model the evolution of the entire term structure, rather than to introduce a specific model for the short rate. The advantage of this framework is that the resulting models are consistent – almost by their very definition – with the initial term structure observed in the market. The main disadvantage is that (except for some special cases, which correspond to short rate models like Hull-White) the HJM framework is difficult to calibrate to market data, and difficult to use for the actual pricing and hedging of instruments. Still, the approach is conceptually attractive, providing a general frame-
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