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Suppose that one want to price an Interest Rate Swap with daily averaging, i.e. the floating leg looks like

$$Floating~Leg = \sum\limits_{i=1}^N P(T_i)\cdot\frac{\sum_{k=1}^m F(t_k, t_k+\delta)}{m}, ~T_{i-1}\leq t_k< T_i$$

It seems like some sort of convexity adjustment is needed there since some of rates are maturing before the natural payment time and some are maturing afterwards. In essense this a mix of cases discussed in Brigo & Mercurio book (13.8.5 Forward Rate Resetting Unnaturally and Average-Rate Swaps) and this question.

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