Hi

I have again two questions which boggles my mind.

First question is simple, but I cannot find an answer for this from anywhere in the text. This is because in book one always makes the simplifying assumption that dates T are assumed to be nice whole numbers, even though they are dates in practise.

So take an example. Assume vol(t) means a forward rate volatility, and the forward rate has been quoted in actual/360 basis (for example).

If there is an integral which needs to be computed

int_{T_0}^{T_p} vol(t)^2 dt = int_{0}^{T_p-T_0} vol(t-T_0)^2 dt

vol here is yearly volatility, but what exactly does T_p-T_0 mean?

I have two alternatives:

It is the euclidean distance between the two dates T_0 and T_p in YEARS.

If this is the case, what does a year mean? Computer stores dates in serial numbers, where usually the difference between two dates is a number which represents the days between the dates. What is the method to convert days to years? Divide by 365?

It is the daycount adjusted dayfraction between dates T_0 and T_p quoted in act/360 basis.

I have a feeling that the second one is true, but I want to make sure.

More generally in equations where there is the difference between two dates, which is the right way to think what the actual number is? Is it always the euclidean distance (in years) or the daycount adjusted alternative, and the right adjustment needs to be figured out from the occasion?

Second question in swaps:

The market convention in EUR market is to assume the floating leg in swaps to be 6M interest quoted in actual/360 basis. The fixed leg pays annually, and the interest is being made in the bond 30/360 basis.

Does this means that only the fixed leg pays interest with 30/360 convention and floating leg pays interest with actual/360 basis? Or is it that also the floating leg pays interest in 30/360 basis even though the interest rates are based on actual/360 basis?

Thanks in advance!