Trying to price a 10Y 10Y forward starting CMS swap. I can match the page CMS01 of ICAP for a 10Y swap and for a 20Y swap.When I take the difference of these 2 swaps shouldn't I be able to price the 10Y swap starting in 10Y?When compared to market quotes it's totally different. I have to admit my convexity adjustment is not using the Pat Hagan Method but just a Hull method with adjusted volatilities.

QuoteWhen I take the difference of these 2 swaps shouldn't I be able to price the 10Y swap starting in 10Y?I may be mistaken but i don't think that taking the difference of those two swaps makes any sense.What is quoted on the page is the spread to Euribor that yields zero present value of the CMS. The spread on the 10y swap has no meaning after 10 years, so there is no point in subtracting it from the spread of the 20y.Suppose the spread on the 10y swaps is 50bp and on the 20y swap is 45bp. The 20y spread can be seen as an average (of some kind) between the spreads on the 10y and the 10y10yfwd. Since the 20y spread is lower than the 10y i would expect it to belower than the 20y. So lesser than 45bp. Maybe around 40bp, but impossible to say more qualitatively....It seems very similar to spot and forward interest rates... If the 10y rate is 6% and the 20y is 5% the forward rate for the period starting in 10y and finishing in 20y isn't 1%, but 4%... (at least if they are instantaneous ones)...Mn... does that sound correct? If so, does it help?

Long of a 10Yr forward 10Yr swap is in principal equal to being long a 20Yr swap and short a 10Yr swap. This structure has a PV of 0, being a combination of two PV 0 contracts. However after ten years, you will have accumulated the differences between the 10 and 20 yr fixed rates, and these will then amortise over the remaining 10 years of the 20yr term to have a value of 0. The rate at which you must make this amortisation gives you the difference between the rate for the 20 yr and the 10yr fdw 10yr. Note that you also need to take into account the compounding of the payment differential over the life of the 10yr swap.You need to build some sort of implied forward LIBOR curve in order to price this correctly. There is more than one way to do this.Of course, if you are pricing a CMS, you then need to rinse and repeat for the entire 10yr life of the foward starting contract.

gc, sorry about that. My explanation was really ridiculous and my sentence did not make sense. Let me make this clear. I am trying to use a blackbox pricer to price a deal. This is kind of experimental... I have limited tools and trying to work out a way to use them for more complex products.I can match the CMS01 page, which means if I am pricing a 3M Euribor leg + quoted spread vs CMS leg I have a Net Value of 0. To do so, instead of using an ATM vol in the Hull convexity adjustment, I have calibrated a kind of fudge added to the ATM. With my method, I can match:swap1: 3M Euribor leg + quoted spread vs 10Y CMS leg of maturity 10Yswap2: 3M Euribor leg + quoted spread vs 10Y CMS leg of maturity 20Yand everything on CMS01.I end up with a modified volatility surface which is an input to the Hull convexity correction.What I am trying to do now is to price the libor + spread vs 10 Y CMS starting in 10Y and maturing in 20Y.In the pricer I am inputting these 2 swaps as a structure, and imply the spread so that the structure is worth 0.Do you see my point?Shouldn't I be able to find a spread close to the market?

Try to implement these papers: -Swaption skews and convexity adjustments, Mercurio-Smiling at convexity: bridging swaption skews and CMS adjustments, MercurioYou can find in fabiomercurio.it

QuoteTo do so, instead of using an ATM vol in the Hull convexity adjustment, I have calibrated a kind of fudge added to the ATM. Of course implementing a proper convexity adjustment is way preferrable, but if you have few resources it might not be possible to do in times that are useful.Still i think you should be able to quote values close to the market using your method (you are practically calibrating the convexity to the market). You should be able to obtain sensible prices for your 10y10yfwd if you price it exactly in the same way as you price a spot CMS swap (only it's a forward starting one, so you don't consider the first 39/40 payments). The only thing you need to do is to provide your own FUDGE to the volatility used in the Hull convexity formulas. What value to use? Let's suppose that to reprice the values in CMS01 for the 10y you add 3vols to the volatility and to reprice the 20y you add 3.5vols to the volatility. The periods are similar and the 20y fudge is greater than the 10y fudge, so you probably want a fudge for your 10y10yfwd to be around 4vols.Do you get anything in the ballpark?If so you might want to insert not the "spot" fudges but forward fudges following a similar algorithm to bootstrapping fudges...Oh dear... this sounds too debatable (and risible) to be written... but worth giving it a bash!...Let me know...

It doesn't look very difficult.If you are long swap 20y and short swap 10y, you can summarize your position as- swap fwd 10y10y [CMS versus E3M + spread(swap20y)]- a string of cash-flows equal to [spread(swap20y) - spread(swap10y)].You then re-balance the NPV of of the 10y running [spread(swap20y) - spread(swap10y)] on the 10y10y fwd swap:[spread(20y) - spread(10y)] * BPV10y / BPV10y10y = Spread_bisThen the quotation of the 10y10 fwd swap will be [Spread_bis + spread(20y)].Hope this helps