Deriving the Asset Swap Spread from Bond and Swap Values

Summary

The document clarifies the valuation signs behind an asset swap spread. In the described arrangement, the investor pays the price of a risky fixed-rate bond and receives its fixed cash flows, while entering a swap that converts those payments into floating-rate payments plus a spread. The floating-rate bond is treated as worth par, and the fixed cash flows are valued using the risk-free fixed-rate bond value.

The answer resolves the original sign confusion by distinguishing which positions are bought or sold. The floating-rate payer is short the floating-rate bond; the relevant present values imply that the spread value equals the risk-free fixed-rate bond value minus the current value of the risky bond. The explanation is an accounting identity for the stated setup, not a full treatment of asset swaps. It relies on the convention that the floating bond is at par and does not detail payment timing, accrued interest, credit-risk modeling, or market-specific conventions.

Key ideas

• The floating-rate payer is short the floating-rate bond in the described asset swap.
• The floating leg starts from a par-value floating bond and adds the present value of the spread.
• The fixed leg compares the risky bond's market price with the value of its fixed cash flows at risk-free rates.
• For this setup, the spread value is the difference between the risk-free fixed-bond value and the risky bond price.
• The derivation depends on the stated valuation conventions.

Tags

# Asset Swap Spreads


# Asset Swap Spreads












This is John Hull's book `Options, Futures and Other Derivatives 9th` `Page 549`

The process of calculating the `Asset Swap Spreads.`

- $1+V$ the discounted value of floating rate paying of `LIBOR+premium`

- $B^*$ the discounted value of fixed rate paying

- $B$ is the current value of fixed rate bond

- $1$ is the current value of floating rate bond(value at par)

As my understanding, floating rate paying will spend $1$ to buy the floating rate bond and receive the money $B^*;$ and fixed rate paying will spend $B$ to buy the fixed rate bond and receive the money $1+V.$

So the relation should be $$-1 + B^* = - B + (1+V),$$ something reverse from the following result, I must misunderstand somewhere?

## Answer by Lliane (score 0)

https://quant.stackexchange.com/a/35809

The asset swap spread is a function of the riskiness of the bond.

> floating rate paying will spend 1 to buy the floating rate bond and receive the money $B^∗$;

If he is the floating rate payer he is short the floating bond, not long.

On the floating rate paying leg he pays $1$ and he receives $1 + V$ (PV of Libor + Spread). The fixed rate receiver (same person) is long the risky fixed rate bond which costs $B$ and its payments (risk free) are worth $B^*$. With this reasoning you can go directly to $V = B^* - B$ by the way (floating rate pay leg present value is $1+V-1 = V$, fixed rate receive leg market present value is $B^* - B$).

Pay $1 + B^*$

Receive $1 + V + B$

Just reorganize $1 + V = B^* + 1 - B$

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.