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3#
发表于 2013-4-4 19:28
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Here is how I do it. It takes an extra minute, but this method was much simplier than the ones presented in the books in my opinion. This will look like a long explanation, but it is actually pretty simple when you understand it and you can do it pretty quick.
The key is to remember that you value a fixed rate bond like you normally would. Then, you independently value a floating security. Keep in mind the floating rate security resets to par at each payment.
First the fixed rate bond:
The interest rate is 5.0% semi-annually. With a notional principal of $10MM, that means two payments of $250,000. The notional principal of $10MM also is returned on the second payment. So I actually right out on the page:
$250,000 + $10,250,000
To calculate the value of the bond, you must discount each of these back. Since this is a 360 day agreement with semiannual payments, from initation payments will come at day 180 and day 360. It says you are 90 days into the agreement, which means the payments are now 90 and 270 days away.
The 90 day rate was 5.0%. That is an annual rate, so you must divide by 4 (4 = 90/360) to get how much to discount over the 90 days = 1.25%. You do the same thing with the 270 rate 5.4% = 5.4%*(270/360) = 4.05%. Now I add those underneath my cashflows:
$250,000/(1.0125) + $10,250,000/(1.0405) = $10,097,947.74
That’s the value of the fixed rate security.
Now the floater:
Again I first figure out the cashflows but remember, it resets to par at each payment. Think of it as the bond matures and returns the principal at each payment, then issues a new security at par if that makes sense.
So they give you the initial rate of 4.8%. That is semi-annual, so the first coupon is $240,000. You have the $10MM notional principal returned with this though, so the actual cashflow is $10,240,000 in 180 days. I write down on the paper:
$10,240,000
Now 90 days later, the rate to discount it at is the same as the 90 day rate for the fixed security (5%/4 = 1.25%).
$10,240,000 / (1.0125) = $10,113,580.25
Now subtract the two:
$10,113,580.25 - $10,097,947.74 = $15,632.51
When I understood this method, the swap section went from being hard for me, to a very very easy chapter. |
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