Convexity Adj and Applicable Floating Int Rate !!!

[Chintan]

Hi David….

I have 2 quick questions…….

Question#1

The FLOATING rate applicable in the Interest Rate Swap is as at beginning of the swap or the rate at the end of each period ?

I found two contradicting answers for this from 2 diff sources and thus this confusion at the 11th hour……..


Question#2

While solving a particular question on convexity adjustment….I found two answers wherein both are right if we consider the difference in formulas wherein in one formuala there is a denominator which has 2 * initial value * Delta Y square …..while for the second formula, the denominator has 1 time initial value * Delta Y square……..

Which is appropriate to use here ???? The former or the latter ????

Kindly reply asap !

Thanks in advance….

Chintan

 

[David Harper CFA FRM]

Chintan,

#1
In a plain vanilla interest rate swap, the floating rate is set (re-set) at the BEGINNING of each swap period. If it helps you to remember the way that i remember this: as Hull says, the first exchange of payments (i.e., six months into the swap) is known at swap inception; that's only possible because floater based on beginning of period rate.

#2
Both/either are correct. You are referring to the convexity MEASURE which, as Fabozzi says, has no real meaning.

Your first MEASURE goes into this formula

convexity ADJUSTMENT = convexity MEASURE x (yield shock)^2 [x 10,000]


Your second MEASURE goes into this formula

convexity ADJUSTMENT = convexity MEASURE/2 x (yield shock)^2 [x 10,000]


Either is appropriate, both are fine. Because the convexity adjustment is the important (risk) measure of sensitivity, the convexity measure just helps you get to the adjustment. (Although I've noticed Fabozzi, who is the authority, has lately gone from writing both methods to just writing the former).

David