标题: Advanced FRA Question [打印本页] 作者: dvilayphet 时间: 2011-7-11 19:34 标题: Advanced FRA Question
So we have to unannualize and reannualize rates, how can we do this without using compounding in our FRA formula? What am I missing?作者: yospaghetti 时间: 2011-7-11 19:34
I don't believe there is any compounding in the FRA formula... Could you be more specific, please?
Are you referring to the pricing or valuation mid-contract?作者: RMontgomery 时间: 2011-7-11 19:34
Well the techinical correct way to do it is to use compounding. For instance, if there is a 90 day rate = 5.0%, that number is annualized. To get the actual amount of interest paid, you raise it to the .25 = 1.23%.
However, with LIBOR rates, it is assumed 360 days are in a year. If you take the ratio of days/360, it will give you a real close approximation of the rate. In this case, 5.0%*(90/360) = 1.25%.
On the real thing, I would first use the technically correct way of compounding. If your answer isn't one of the listed choices, recalculate using the approximate measures.作者: luda002 时间: 2011-7-11 19:34
but with LIBOR there is NO ANNUALIZING. Look it up.
it is an ADD-ON Rate, not a compounded rate.
Schweser does throw in a few problems on SWAPs with Spot Rates - but that is just Schweser.
There is no annualizing.
1+0.05*90/360 = 1.0125
(1.05)^0.25 = 1.01227
not too much of a difference... but on bigger amounts and multiplied / divided could make a lot of difference to the answer.
CP作者: flyinggirl 时间: 2011-7-11 19:34
Ok so the technically correct way is to multiple by the respective d/360 and NOT compund at that ratio?作者: Houjichasan 时间: 2011-7-11 19:34
cpk, does "add-on" rate just mean you use simple interest and not compound interest?作者: giants2010 时间: 2011-7-11 19:34
A couple things. "Add-on interest" refers to the fact that LIBOR is not quoted at a discount where Treasury bills are, which is called "discount interest". (CFAI, Vol. VI, pp. 14,15)
Next, here is the CFA formula for valuing an FRA mid-contract to the long (ibid, pp. 37)
Vo = Notional Principal multiplied by --->
1 / [1 + (new short-term rate x days/360)] - [1 + (FRA rate x days/360)] / [1 + (new long-
term rate x days/360)]作者: 5566 时间: 2011-7-11 19:34
I remember from Lvl I that the way a rate is quoted is by convention .
Strictly speaking the TVM calculation would NOT treat a rate over a longer period as a simple linear increase over a shorter period:
R1 = 1+ (R * 90/360)
R2 = 1+ (R * 180/360)
The add-on rates are simple multiples of the base annualized rate at a point of time.
That's the way the LIBOR rates are quoted and used . So lets not argue about that.
TVM would say:
R2 = Sqrt( (1+R1)^2) - 1
But LIBOR does not use a TVM calc for quoting , it uses the above "add-on" way.
