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If I treat the 2 legs as bonds, and I want to calculate the present value somewhere between 2 payment date, should I calculate accrued interest?

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When you sum up all the discounted cash flows, you effectively a "dirty price" (i.e., inclusive of "accrued interest"). This quantity is used for marking to market or unwinding. You don't need to worry about "accrued interest" separately.

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  • $\begingroup$ Does that mean in a swap, the accrual interest for both legs are cancelled? $\endgroup$ – SmallChess Apr 16 '16 at 13:34
  • $\begingroup$ @StudentT They won't cancel out completely, since the flt/fixed rates, day count conventions, payment frequency are all different. $\endgroup$ – Helin Apr 16 '16 at 16:30

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