Calculating Asset Swap Floating Coupons with Day-Count Fractions
Summary
The example explains how to calculate floating coupons in an asset swap when payment periods do not match a simple half-year assumption. Each coupon uses the annual LIBOR fixing plus the quoted spread, multiplied by notional and the accrual fraction determined by the stated day-count convention. With Actual/365, the fraction is the number of actual days in the period divided by 365.
The first coupon is smaller because its initial accrual period is short; later periods can also differ slightly from one half-year when measured in actual days. The explanation reproduces coupon amounts from the cited example and notes a possible calendar issue: a scheduled payment date falling on a weekend might be adjusted, though it is unclear whether the asset swap follows adjusted dates or the bond’s unadjusted coupon dates. It focuses on the floating coupons and does not resolve the other price and swap-value questions raised.
Key ideas
- Floating coupons use the applicable reference rate plus the asset swap spread.
- Multiply that annual rate by notional and the period’s day-count fraction to obtain the coupon.
- Actual/365 accruals can differ from a simple fraction such as one-half year.
- A short initial accrual period explains why the first floating payment is smaller.
- Business-day adjustments may affect dates, and the example leaves the convention uncertain.
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# Understanding Asset Swap Spread Example # Understanding Asset Swap Spread Example 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 by Dimitri Vulis (score 2, accepted) https://quant.stackexchange.com/a/60232 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?)
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