Computing the asset swap spread

For the purpose of the following, we assume we have constructed a market curve of Libor discount factors where z(t) is the price today of $1 to be paid at time t.

From the perspective of the asset swap seller, they sell the bond for par plus accrued interest ("dirty price"). The net up-front payment has a value 100-P where P is the full price of the bond in the market. Both parties to the swap are assumed to be AA bank credit quality and so these cash flows are priced off the Libor curve. We cancel out the principal payments of par at maturity. For simplicity we assume that all payments are annual and are made on the same dates.

As is standard for swaps, the break-even asset swap spread A is computed by setting the present value of all cash flows equal to zero.

1. From the perspective of the asset swap seller the present value is:

100 - P + Coupon (Fixed Part) - Coupon (Floating Payment)

The floating payment part equals ${\displaystyle \Sigma _{i}\Delta _{i}(L_{i}+A)\ z(t_{i})}$, where ${\displaystyle \Delta _{i}}$ is the accrual factor in the corresponding basis, ${\displaystyle t_{i}}$ is the term of time period and ${\displaystyle L_{i}}$ is the Libor rate set at time ${\displaystyle t_{i-1}}$. The fixed and floating sides may have different frequencies.

2. We then solve for the asset swap spread A such that the present value is zero.

On a technical note, when the asset swap is initiated between coupon dates, the asset swap buyer does not pay the accrued interest explicitly. Effectively, the full price of the bond is at par. At the next coupon period the asset swap buyer receives the full coupon on the bond and likewise pays the full coupon on the swap. However, the floating side payment, which may have a different frequency and accrual basis to fixed side, is adjusted by the corresponding accrual factor. Therefore, if we are exactly halfway between floating side coupons, the floating payment received is half of the Libor plus asset swap spread. This feature prevents the calculated asset swap spread from jumping as we move forward in time through coupon dates.

Market Asset Swap

In the market asset swap, the net upfront payment is zero. Instead the notional on the Libor side equals the price of the bond and there is an exchange of notionals at maturity.