# By swap valuation, is accrued interest calculated?

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?

## 1 Answer

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.

• Does that mean in a swap, the accrual interest for both legs are cancelled? – SmallChess Apr 16 '16 at 13:34
• @StudentT They won't cancel out completely, since the flt/fixed rates, day count conventions, payment frequency are all different. – Helin Apr 16 '16 at 16:30
• Could you give an explicit formula? As far as I can see, the price at time $T_0 < t < T_1$ should be the sum of prices of a forward starting swap (i.e. the swap with the first resent date $T_1 > t$) and $P(t,T_1)\tau(T_0, t)(L(T_0, T_1) - K)$ where this last term is the PV of the accrued interest since the last resent date $T_0$ to be paid at time $T_1$. – Confounded Oct 1 '20 at 8:58