Why Asset Swap and I-Spread Measures Do Not Convert Directly
Summary
The document asks whether a closed-form conversion exists between an asset swap spread and an I-spread. It describes the I-spread as a bond yield spread against a matched-maturity vanilla swap rate, associated with credit exposure after hedging interest-rate sensitivity. It characterizes the asset swap spread as incorporating the bond’s price and cash flows relative to the swap curve, so a bond trading far from par can cause the two measures to differ substantially.
The response expresses the asset swap spread as the difference between a curve-discounted bond price and its market price, divided by the swap annuity or PV01. It explains that the asset swap’s repayment leg continues to maturity even if the bond defaults, while the spread still reflects credit risk through the bond’s market price. The response does not give a conversion formula and says the I-spread definition needs more precision, including whether the swap terminates with the bond. The comparison therefore depends on product conventions and exact trade structure.
Key ideas
- The I-spread compares a bond yield with a matched-maturity swap rate.
- The asset swap spread reflects the bond’s market price relative to its value discounted on a swap curve.
- The asset swap spread can diverge from the I-spread when the bond price is far from par.
- The asset swap spread can be represented using the price difference divided by the swap leg’s PV01.
- A direct conversion requires precise definitions of the I-spread and the swap’s termination terms.
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Full text
# Compute I-spread from ASW-spread (or vice versa)
# Compute I-spread from ASW-spread (or vice versa)
The I-spread ("mid swap spread" or yield-yield spread) is a standlone measure of credit risk, a security against matched maturity vanilla swap rate. Consider a package in which the investor receives security's coupon and takes credit risk: interest rate exposure is delta-hedged with a matched-maturity swap.
The asset swap (ASW)-spread is a measure of total return, because coupon and principle cashflows are discounted at prevailing swap rate. Upfront principle, which may be large if the security price is far from par, means that the ASW-/I-spreads are often highly divergent.
Is there a closed form soln to convert from one to the other?
## Answer by Dom (score 1)
https://quant.stackexchange.com/a/29537
The asset swap spread is the amortised repayment of the difference in price between a specific credit risky bond and the price of that same bond discounted on the Libor swap curve. It is written as
$D=\frac{P_{Libor}-P}{\rm PV01}$
where $PV01$ is the the annuity of the swap floating leg and $P_{Libor}$ is the discounted bond price on the Libor curve and $P$ is its actual market price.
The repayment is risk free in the sense that the swap leg of the asset swap must continue to the maturity of the asset swap i.e. the swap does not cancel even if the asset defaults. As it depends on the price in the market of the bond, it does depend on the credit risk of that bond which is embedded in its market price and so it is risk-adjusted. As it determines cash flow sizes in a real trade, the asset swap spread is more than just a measure of credit risk.
Your definition of an I-swap is not complete. Can you explain exactly how it is calculated. Does the swap cancel with the bond ?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.