Hi Mike,

It's a great point, they seem connected, but it's two different things. If we look at the way Hull tends to (with precision) characterize rates, it looks as follows (eg):

"4.0% per annum with [continuous | annual | quarterly | etc ] compounding"

The day count convention (or day count basis) is not here specified but, in a way, resides "within" the "4.0% per annum" and is SEPARATE from the compound frequency.

Consider Hull's instructive example 6.3, where he adjusts a Eurodollar futures rate into its equivalent forward rate.

He starts with a Eurodollar quote = 94 which, b/c it's a 90-day money market instrument, refers to an interest rate that is: 6.0% per annum (i) on an actual/360 day count basis with (ii) quarterly compounding

As he needs to subtract a convexity adjustment that just happens to be expressed in "actual/365 with continuous compounding." So he does this:

=365/90 * LN(1+6%/4) = 6.03816%; converting 6% continuous to quarterly, a calculation which has tended to give confusion

It can be unpacked, to illustrate there are two aspects:

= 4*LN(1+6%/4) = 5.9554%; i.e. convert a quarterly to continuous compound frequency

= 5.9554% * 365/360 = translate an actual/360 (LIBOR) to actual/365 day count so the subtraction is "apples to apples"

**That is three LIBOR rates, all valid**
Similarly, while 6.0% LIBOR generally quotes in actual/360 day count (

http://en.wikipedia.org/wiki/London_Interbank_Offered_Rate), this 6.0% per annum does not tell us which compound frequency and allows for continuous or discrete. Generally, we take guidance from the instrument: a semi-annual bond implies semi-annual; a 90-day ED futures implies quarterly; but the implied frequencies don't stop us from over-riding with a continuous

I hope that helps, David

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