Credit-default swaps are well established in the debt market as hedging instruments against credit risk and to enable market participants to establish a synthetic short position in a specific reference credit and implement credit-trading strategies outside the cash markets. The most common method of pricing default swaps is by recourse to the asset-swap spread of the reference credit, as the default-swap premium should, in theory, be equal to the asset-swap spread of the reference asset. We first consider the use of this technique, before looking at the issues arising that cause these two spread levels to differ.
Asset-Swap Pricing
Credit derivatives are commonly valued using the asset-swap pricing technique. The asset-swap market is a reasonably reliable indicator of the returns required for individual credit exposures and provides a mark-to-market framework for reference assets as well as a hedging mechanism. A par asset swap typically combines the sale of an asset such as a fixed-rate corporate bond to a counterparty, at par and with no interest accrued, with an interest-rate swap. The coupon on the bond is paid in return for LIBOR, plus a spread if necessary. This spread is the asset-swap spread and is the price of the asset swap. In effect the asset swap allows market participants that pay LIBOR-based funding to receive the asset-swap spread. This spread is a function of the credit risk of the underlying bond asset, which is why it may be viewed as equivalent to the price payable on a credit-default swap written on that asset.
The generic pricing is given by:
Ya = Yb- ir
where:
Ya is the asset-swap spread
Yb is the asset spread over the benchmark
ir is the interest-rate swap spread.
The asset spread over the benchmark is simply the bond, asset, redemption yield over that of the government benchmark. The interest-rate swap spread reflects the cost involved in converting fixed-coupon benchmark bonds into a floating-rate coupon during the life of the asset, or default swap, and is based on the swap rate for that maturity.
The theoretical basis for deriving a default-swap price from the asset swap rate can be illustrated by looking at a basis-type trade involving a cash market reference asset, bond, and a default swap written on the bond. This is similar in concept to the risk-neutral or no-arbitrage concept used in derivatives pricing. The theoretical trade involves:
* a long position in the cash market floating-rate note (FRN) priced at par, and which pays a coupon of LIBOR + X basis points;
* a long position--bought protection--in a default swap written on the same FRN, of identical term to maturity and at a cost of Y basis points;
The buyer of the bond is able to fund the position at LIBOR. In other words, the bondholder has the following net cash flow:
[100 100] + [(LIBOR + X) (LIBOR + Y)]
or X-Y basis points.
In the event of default, the bond is delivered to the protection seller in return for payment of par, enabling the bondholder to close out the funding position. During the term of the trade the bondholder has earned X Y basis points while assuming no credit risk. For the trade to meet the no-arbitrage condition, we must have X = Y. If X ‡ Y the investor would be able to establish the position and generate a risk-free profit.
This is a logically tenable argument as well as a reasonable assumption. The default risk of the cash bondholder is identical in theory to that of the default seller. In the next section we illustrate an asset-swap pricing example, before looking at why in practice there exist differences in pricing between default swaps and cash market reference assets.
Asset Swap Pricing Example
XYZ plc is a Baa2 rated corporate. The seven-year asset swap for this entity is currently trading at 93 basis points; the underlying seven-year bond is hedged by an interest-rate swap with an Aa2 rated bank. The risk-free rate for floating-rate bonds is LIBID minus 12.5 basis points, assume the bid-offer spread is six basis points. This suggests that the credit spread for XYZ plc is 111.5 basis points. The credit spread is the return required by an investor for holding the credit of XYZ plc. The protection seller is conceptually long the asset and so would short the asset to hedge its position. This is illustrated in the diagram. The price charged for the default swap is the price of shorting the asset, which works out as 111.5 basis points each year.
Therefore we can price a credit-default swap written on XYZ plc as the present value of 111.5 basis points for seven years, discounted at the interest-rate swap rate of 5.875%. This computes to a credit swap price of 6.25%.
| Reference | XYZ plc | |
| Term | Seven years | |
| Interest-rate swap rate | 5.875% | |
| Asset swap | LIBOR plus 93bps | |
| Default swap pricing: | ||
| Benchmark rate | LIBID minus 12.5bps | |
| Margin | 6bps | |
| Credit-default swap | 111.5bps | |
| Default-swap price | 6.252% |
Pricing differentials
A number of factors observed in the market serve to make the price of credit risk that has been established synthetically using default swaps to differ from its price as traded in the cash market. In fact identifying, or predicting, such differences gives rise to arbitrage opportunities that may be exploited by basis trading in the cash and derivatives markets. These factors include the following:
* bond identity: the bondholder is aware of the exact issue that he is holding in the event of default, however default swap sellers may receive potentially any bond from a basket of deliverable instruments that rank pari passu with the cash asset; this is the delivery option afforded the long swap holder;
* the borrowing rate for a cash bond in the repo market may differ from LIBOR if the bond is to any extent special; this does not impact the default-swap price which is fixed at inception;
* certain bonds rated AAA, such as U.S. agency securities, sometimes trade below LIBOR in the asset-swap market; however a bank writing protection on such a bond will expect a premium, a positive spread over LIBOR, for selling protection on the bond;
* depending on the precise reference credit, the default swap may be more liquid than the cash bond, resulting in a lower default-swap price, or less liquid than the bond, resulting in a higher price;
* default swaps may be required to pay out on credit events that are technical defaults and not the full default that impacts a cash bondholder; protection sellers may demand a premium for this additional risk;
* the default swap buyer is exposed to counterparty risk during the term of the trade, unlike the cash bondholder.
For these and other reasons the default-swap price often differs from the cash market price for the same asset. Therefore banks are increasingly turning to credit pricing models, as used to model interest rates, when pricing credit derivatives.
This week's Learning Curve was written by Moorad Choudhry, a senior fellow at the Centre for Mathematical Trading and Finance at City University Business School in London. It is based on his book: Bond Market Securities published by FT Prentice Hall.
