SERVING THE QUANTITATIVE FINANCE COMMUNITY

human909
Topic Author
Posts: 3
Joined: August 30th, 2006, 11:11 pm

### Just a quick convexity question

Do you need to use convexity adjustments when calculating the forward rates from swap rates and LIBOR rates? From what I have read convexity adjustments are used when futures are used and are a result of the daily settlement of futures.Thanks, for your help guys

gwd999
Posts: 2
Joined: October 25th, 2002, 11:54 pm

### Just a quick convexity question

What you read / heard is absolutely right. No adjustements needed for Swaps and Libor!

manolom
Posts: 238
Joined: March 14th, 2006, 2:52 pm

### Just a quick convexity question

The forward rate that applies to a interval of time ending at T is a martingale under Q^T, the measure that has P(·, T) as the numeraire, thus no adjustment is required. But the same forward rate is not a martingale under Q^(T-1), so a convexity adjustment is needed. This is used, for example, when pricing in-Arrears swaps. The file www.cam.wits.ac.za/mfinance/projects/nevena.pdf is quite clear and explains very well this issue.

human909
Topic Author
Posts: 3
Joined: August 30th, 2006, 11:11 pm

### Just a quick convexity question

Thanks manolom, I think I understand it now, that pdf was quite useful. I have also done much further reading. But one more question to confirm.Do I need convexity adjustments in this case?Suppose I was pricing a capped floating rate note, whose floating rate were coupons paid semiannually based on the 6month LIBOR as at 6 months ago.Would it be correct to price this by calculating the coupons using forward rates derived from the zero curve without convexity adjustments. And then discount these payments with the zero curve. I assume that a convexity adjustment isn't need as the coupons are paid in line with the natural time lag of the 6month LIBOR. And of course since it is a capped FRN i'll need to include the appropriate caplets in the pricing as well. Thanks again guys!
Last edited by human909 on September 17th, 2006, 10:00 pm, edited 1 time in total.

manolom
Posts: 238
Joined: March 14th, 2006, 2:52 pm

### Just a quick convexity question

QuoteOriginally posted by: human909 a convexity adjustment isn't need as the coupons are paid in line with the natural time lag of the 6month LIBORYou're right. I think last chapter in Pelsser's book also adresses the issue of convexity.

Alkmene
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Just a quick convexity question

but why"But the same forward rate is not a martingale under Q^(T-1), "I do not understand how to see that?Alk