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I was reading Pat's Paper (Convexity conundrums), which is really clear...I would like to learn more on the replication of CMS Caplets with vanilla Payers swaptions... does anyone have hints?

The only slight pb with the replication is that swaptions are settled at their maturity whereas CMS caplets pay according to the caplet rules i.e have a delayed payment. Not adjusting for that will result in call-put parity breaches when valuing a CMS swap with coupons capped/floored....Appart from that: Suppose K0 is the strike of your CMS option.Take K1, K2, K3,.... increasing strikes and suppose you are looking at a portfolio of swaptions like this w0.Swpt_0 + w1.Swpt_1 + w3.Swpt_3 + ......Where: wi is the amount of Swpt_i you use and Swpt_i is the vanilla swaption which strike is Ki.Finding w0:You want w0 so that if S equal to K1, the payoff of the porfolio is matching the CMS caplet.i.e you want w0 so that w0.(K1 - K0) + 0 + 0 + .... = K1 - K0==> w0 is the only unkwon here Finding w1:You want w1 so that if S equal to K2, the payoff of the porfolio is matching the CMS caplet.i.e you want w1 so that w0.(K2 - K0) + w1.(K2 - K1) + 0 + .... = K2 - K0==> w1 is the only unkwon here since you have w0 alreadyFinding w2:You want w2 so that if S equal to K3, the payoff of the porfolio is matching the CMS caplet.i.e you want w2 so that w0.(K3 - K0) + w1.(K3 - K1) + w2.(K3 - K2) + 0 + .... = K3 - K0==> w2 is the only unkwon here since you have w0 and w1 alreadyetc.....

Hoops I forgot the PVO1s in the swaptions payoff of course!w0.PVO1(K1 - K0) + 0 + 0 + .... = K1 - K0w0.PVO1(K2 - K0) + w1.PVO1(K2 - K1) + 0 + .... = K2 - K0w0.PVO1(K3 - K0) + w1.PVO1(K3 - K1) + w2.PVO1(K3 - K2) + 0 + .... = K3 - K0PVO1 is has to be approximated by function(Ki) when S is Ki.That is another pb with this replication....

wow thanks for that clear answer... I ll have to digest it now!

Where can I find the Pat's paper "Convexity Conundrum:..."?Do you have a soft copy?Thanks.

Hello,How do you find the PV01's? To replicate the CMS caplet payoff I'm first trying to find the curve of a swaption payout vs. the underlying swaprate. How I am doing it now is by choosing several values of the swap rate, then:PV01 = ( P(0,t1) - P(0,t2 ) ) / swaprate.where t1 is the swaption maturity and t2 the end of the underlying swap. But P(0,t1) and P(0,t2) are held fixed... which is a problem.Thanks in advance!

Also, if anyone could point me to a paper on this topic, that would be much appreciated.Thanks!

TryG. Amblard and J. Lebuchoux "The Relationship between CMS options and the Smile", RISK Magazine, Sep. 2000F. Goodwin "Buy a Dollar for 80 cents - EUR CMS10 Caps are Mispriced", Lehman Brothers Global Financial Strategies, Aug. 2000

Thanks Caroe. Do you have any ideas about finding the PV01s?

Thanks Caroe. Do you have any ideas about finding the PV01s?

The best way to start thinking about this is to model CMS caps that fix in arrears so we don't have to think about discounting between the fixing date and the pay date.Cash settled Payers swaptions in Euro's pay out according to the following formula (USD swaptions are PV settled so curve risk here too)Payout = Notional * MAX(Rate - strike,0) * a *(a^n-1)/(a-1) where a = 1/1+r and n is maturity of underlying swap.All you need to do now is to match the payout of the CMS cap by choosing the appropriate notional of swaption at each of a whole set of strikes

F. Goodwin "Buy a Dollar for 80 cents - EUR CMS10 Caps are Mispriced", Lehman Brothers Global Financial Strategies, Aug. 2000I like that one. Did anybody make money following Lehman's advice?

Hi there do you have these articles ?

Hi there,also interested but could not find these on the net...Cheers Lapsilago

Convexity Conundrums paper can be found here. HTH