ST6 Sept 06 Q3ii)

On the off chance I'm not the only one doing last minute past papers...

I can't follow the examiners' solution to Q3ii). They seem to be worried about correlation between 1-year and 5-year ZCB rates. What 1-year rate is that? The only one I was using was the one at time 0 which is known.

Unlikely I know, but if anyone should happen to look at it this evening and knows the answer it would be much appreciated!
L
ETA: Hull p615

 

That was one of the questions which is contributing to putting me off ST6 exams...

Anyway, the ActEd solution gave the direct use of Black's model, which is what I went for and is, as ActEd pointed out, the official solution (I wonder if it would have gained any marks in the exam though). What the examiner is trying to say, as I understand it, is that the value now of the 5-yr bond is directly linked to the 5-yr spot rate of interest; and to value the option on a risk neutral basis (which the Black's model uses), you have to use a discount factor based on the 1-year spot rate (since the option matures in 1 year's time); this is the ZCB rate the examiner's referring to. But because the two rates are correlated, if we just changed the underlying in the BS model from a share to a bond, the volatility wouldn't be correct if we just used the one as applicable to the 5-yr rate; therefore we must use a modified version which takes into account of the correlation between the two rates in order for this to work.

I hope that might help a little...

 

Thankyou very much - i did catch this this morning and it was most reassuring, as I did use the Black model for that question.
L