Understanding Asset Swap Spread Example

Question

Here is an overview of the asset swap spread I found online: https://www.deriscope.com/docs/AssetSwaps_LehmanBrothers_2000.pdf
I can't seem to make sense of the numbers in this example:

Specifically, how is the swap floating side calculated? I tried using the notional 10m multiplied by the libor rate + spread and divide by 2 (since semi-annual frequency) but can't get the exact numbers, so I think I am missing something here. In addition, why is the first floating payment only $27,738? My last question is in the summary at the bottom of this example, my guess is that the full price comes from the bond price 101.70% + the accrued interest 2.34375%, but that still doesn't add up to the full price shown here, and I am also hoping to understand what the fixed side of swap (-15.834%) as well as the floating side of swap (11.787%) mean and how are they calculated? If anyone can share some good resources/materials for understanding the basics of asset swap spread, that would be greatly appreciated as well.

Answer 1

All the floating coupons are daycounted. Note that it says Floating Basis: Actual/365. (This is the usual daycount convention for GBP and some other currencies, but for USD the usual daycount convention would rather be Actual/360.)

The first period from October 20, 1999 to November 20, 1999 is odd, short, only 31 actual days. Year fraction 31/365 is 0.084931507 of a year - approximately 1/12, but we are trying to be exact.

LIBOR is 0.02742 plus spread 0.00524 is 0.03266 annually. Multiplying this annual rate by the year fraction and the notional, we get $27.73863014.

The second period November 20, 1999 to May 20, 2000 is 182 actual days. Dividing by 365, the year fraction is 0.498630137, which is not quite 1/2. LIBOR is 0.03771 plus spread 0.00524 is 0.04295 annually. Multiplying this annual rate by the year fraction and the notional, we get $214.1616438, etc.

(We reproduce the numbers in the Lehman paper. However I have a feeling that in real life, since November 20, 1999 was a Saturday, it might get bumped to the next Monday, so the first coupon would accrue until Monday. Or maybe for asset swaps they use unbumped bond coupon dates?)