Lets say we have average/asian swap whose floating leg payoff is dependent on the arithmatic average of the forward rates. Would these forward rates require convexity/timing adjustments? How would these adjuatments look like in a negative rate environment. Lets say this is a EUR swap.
Any reference to a paper/book would be very helpful. Thanks in advance for your help.
Assuming it is a straight up swap with no optionality involved, you can decompose the floating leg into a sum of the reset rates, each of which will (at least in principle) require a convexity adjustment to the extent that the actual payment period is different from the natural one that the reset refers to. Rates being negative doesn't particularly change anything, although it obviously makes a mockery of any model that can only handle positive rates, e.g. a lognormal rate model. By far the simplest approach, especially in the presence of negative rates, would be a Gaussian model, where the convexity adjustment is analytical.