European Options on Stocks 13.2 Providing a dividend yield We get the same probability distribution for the stock price at time T in each of the following cases 1. The stock starts at price so and provides a dividend yield =q 2. The stock starts at price Soe q l and provides no income
The Two-Factor Hul-white Model (equation 24.1, page 571) dx=0(0)+u-ax dt +o,dz1 du= -but +o,dz, where=f(r and the correlation between dz, and dz, is p The short rate reverts to a level dependent on u, and u itself is mean reverting
Company a buys default protection from b to protect against default on a reference bond issued by the reference entity, C A makes periodic payments to In the event of a default by c A has the right to sell the reference bond to B for its face value
Credit ratings In the s&P rating system, AAA is the best rating. After that comes AA, A BBB. BB.B. and ccc The corresponding Moody's ratings are Aaa. Aa,a. Baa, Ba.b. and caa Bonds with ratings of BBB (or Baa) and above are considered to be investment grade
Why Interest rate Derivatives are Much more difficult to value Than Stock Options We are dealing with the whole term structure of interest rates; not a single variable The probabilistic behavior of an individual interest rate is more complicated than that of a stock price Options, Futures, and Other Derivatives, 5th edition C 2002 by John C. Hull
Long Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future want to lock in the price
