If you were asked to pay fixed on a 10 year swap 10years forward, your natural hedge might be to receive fixed on a 20 year swap and pay fixed on a 10 year swap. But then in a positive curve you are effectively receiving known amounts for the first ten years, and then paying known amounts from years ten to twenty. So in some sense you are borrowing money, and I heard someone saying you need to use the 'basis swap adjusted curve' to "account for this", but didn't catch the finer details... I can see that if just use just the libor curve to price the 10y x 10y we haven't accounted for these amounts we borrow. For instance, if you are a usd based bank and you are able to borrow currency (say yen) at below yen libor...(for example using a basis swap)..then we shouldn't be too happy to be effectively paying yen libor to borrow (implicitly through the forward swap)How should I account for this in my pricing? Should I discount the known cashflow differences using a 'basis swap' adjusted curve and then adjust the original 10y x 10y price (calculated from the standard libor curve), or just use the 'basis swap' adjusted curve from the beginning and not even have to bother with the original libor curve? Would they give the same answer? Do forward swaps trade in the market at levels different to what one might expect if you used the standard libor curve?

Don't have the time to go into details, but here is something fun to think about. For illustration purposes assume annual swap coupons and fixed side payments made on an equal coupon basis (i.e. coupon rate divided by the payment frequency). Suppose the 10-year par swap coupon is X and the 20-year rate is Y, where Y > X. As you've noted, receiving fixed for 20 years and paying fixed on 10 years leaves you with known cash flows in years 1 to 10. Instead of using equal notional principals, pay fixed on Y/X units of notional in the 10-year per unit notional in the 20-year. Now play with this...

the swap market incorrectly assumes that borrowing and lending occur at LIBOR....this is problematic in that it is unrealistic, and many houses have recently switched to using two curves: one for forward rates, and one for disounting cashflows......

thanks

Link with a thread (still unanswered) on another forum..How does your 10y10y fluctuates with fluctuations (lets say 1bp) of the 10y and 20y ppoint of the curve?I'm interested to see how a move of 1bps on either 20y or 10y point affects your 10y10y. My guess is that it wont be a 1bps move but how do you work it out?Cheeers and happy new year all!