Swap curve

[echo20]

Mark's replies to my other questions were too good - hence need to ask some more! -->

Chap 22, p.24. Please can someone explain how the swap yield curve is defined and why it provides a proxy for the risk free rate? I understand the government bond yield curve / zero coupon bond yield curve (i.e. collect market prices of bonds, calculate GRYs, plot curve – reasonably risk free because of low default risk of govt bonds), but don’t see how you can do the same with swaps because they’re not so standard (e.g. won’t a 3% fixed rate swap be priced differently to a 5% fixed rate swap based on the same nominal amount?) Help!

 

[Mark Willder]

Chap 22, p.24. Please can someone explain how the swap yield curve is defined and why it provides a proxy for the risk free rate? I understand the government bond yield curve / zero coupon bond yield curve (i.e. collect market prices of bonds, calculate GRYs, plot curve – reasonably risk free because of low default risk of govt bonds), but don’t see how you can do the same with swaps because they’re not so standard (e.g. won’t a 3% fixed rate swap be priced differently to a 5% fixed rate swap based on the same nominal amount?) Help!

Yes, you're right, swaps are sold over the counter and so are not standardised. However, swaps are generally priced to have zero initial value.

So one party might swap floating interest (based on LIBOR say) with fixed interest of 5% for 10 years. The 5% is determined so that the contract has zero initial value.

Banks are surveyed each day for the swap quotes they gave that day for different terms. This information is then used to generate the swap yield curve - in our example we have a 5% yield for the 10 year term.

If the swap curve moves too far away from the bond curve then arbitrage opportunities will emerge. So we would expect the swap curve to be a reasonable proxy for the gilt curve.

Best wishes

Mark

 

[echo20]

Thanks for clearing up my misunderstanding, Mark. Couple of follow-up questions:

1. Presumably the banks include a profit margin when they price the swaps, so when you say swaps are priced with zero initial value, do you mean this margin is negligibly small?

2. What are the main arguments for using the swap curve instead of the gilt curve for a proxy to the risk-free curve (you say the swap curve is a reasonable proxy to the gilt curve, but presumably there's an argument to say that it's actually the better risk-free proxy)?

Thanks a lot.

 

[Mark Willder]

1. Presumably the banks include a profit margin when they price the swaps, so when you say swaps are priced with zero initial value, do you mean this margin is negligibly small?

Yes, banks charge a fee to make a profit. This fee can be charged as an adjustment to the LIBOR rate exchanged on the floating leg.

For example, we may think that swapping variable LIBOR for fixed 5% is a fair swap for a 10 year term. The bank will quote 5% and this is what the swap curve will show.

However, the contract will actually be for LIBOR plus 10 basis points say. So the bank will receive an extra 0.1% in interest as a loading for profit.

2. What are the main arguments for using the swap curve instead of the gilt curve for a proxy to the risk-free curve (you say the swap curve is a reasonable proxy to the gilt curve, but presumably there's an argument to say that it's actually the better risk-free proxy)?

The CFO Forum gave the following justification for using the swap curve instead of the gilt curve.

ADVANTAGES

Swap markets are more liquid than government bond markets.

Swaps are synthetic instruments which do not suffer from systematic distortions due to insufficient supply or regulatory factors.

Swap prices are consistent with how traded options are quoted which is the basis for the market-consistent valuation approach.

Many companies are already using swaps and this is aligned with where the market appears to be heading.

The use of swaps is consistent with using implied volatilities.

DISADVANTAGES

Swap yields contain a small margin for credit risk.

In some markets (for example, in Asia), swaps are not available at long (e.g. over 10 years) durations or at all.

Best wishes

Mark