Class #06: Thursday 06-Dec-2012 and Saturday 08-Dec-2012
Questions for assignment due at the beginning of this class:
Fixed income derivative questions (re-post 05-Dec-2012)
Template for the HJM (re-posted on 02-Dec-2012)
HJM and a call option (posted 23-Dec-2012)
Make sure to read this paper:
Teaching note on HJM
SKIP the calculus and go straight to page 9
Discounting example in Excel
Template for 2nd half of class (please bring this)
Note that the notation in the paper and our class are slightly different. I'm using a notation that we believe is more helpful. To "translate" between the two, we have: The "f(0,1)" on p.9 of the paper is our "f(0,1,2)" in my notation.
Reading the derivations on p.1 to p.8 may add confusion rather than answer questions. Clark is reading it now and he is confusing me.
Remember that ALL rates are given as CCRs. Even a 6% one-year return means using "exp(rt)" or "exp(0.06*1)"
Remember you can discount with spot rates or with forward rates. I've attached an example that might help you.
Once you make the HJM tree, do not mess with it. Unlike equity options, you don't want to play with the interest rate tree. The reason is that the tree should be arbitrage-free. If you mess with it, there is no guarantee it will remain arbitrage-free.
To answer Q.2, do not mess with the rate tree. Instead, right out payments you expect to receive when holding this annuity. If rates are capped, then the payments are also capped. Therefore, mess with the payments to reflect the cap (and not the rates).
Other papers on interest rate derivatives:
Haugh notes on HJM (lots of math)
Benninga and Wiener
Klose and Yuan
Screenshots of Mark's HJM model
Screenshot #1 ( now one page only; re-posted 02-Dec-2012 )