Pricing of Credit Default Swaps

Pricing based on Cash Market credit spreads.

41. A credit default swap is a transfer of credit risk to the protection seller. The pricing must therefore, be based on credit spreads in the Cash Market. Besides the cash market, spreads in the futures markets and the swap markets play an important part in influencing prices. Market liquidity and the ability of the market maker to finance a hedging transaction also influence prices of default swaps.

42. When an investor purchases an asset that includes credit risk, the return on the investment includes a spread premium over the risk-free rate to compensate for the risk of default and loss (as well as a liquidity premium). Credit spreads for many financial assets are readily observable in the marketplace.

43. Since credit default swaps represent exchanges of credit risk between counterparties, intuitively they should be (and frequently are) priced based on credit spreads on cash market benchmarks. More specifically, the pricing is driven by a combination of cash market credit spread levels and the market maker's ability to finance a hedging transaction in the cash market.

44. For example, recently four-year default swaps on American Express (Aa3/A+) were bid at 28 bp and offered at 42 bp. (A dealer would pay a 28 bp annual premium to buy protection, and sell protection in return for a 42 bp annual premium.) A roughly comparable maturity American Ex-press debenture (6 ¾% of June 2004) was offered (on an asset swap basis) at LIBOR + 17 bp and bid at LIBOR + 28 bp (see table below).

If a dealer purchases protection, it can generate income to pay this premium by purchasing the reference asset on an asset swap basis (to isolate credit risk) and financing the position either at its borrowing cost or in the repo market. The breakeven financing rate is quite simply the asset swap yield (5.17%) less the default swap premium (28 bp), or 4.89%. If the dealer can obtain cheaper financing it earns positive carry, or alternatively, can afford to pay a higher premium. If the reference asset cannot be financed in the repo market, as in India, then the pricing of the default swap will be driven by the market maker with the most favourable cost of funds -typically a highly rated bank. Other market makers with higher cost of funds must accept negative carry if they buy protection.

If a dealer sells protection, it can hedge its exposure by borrowing and selling the reference asset and investing the cash proceeds in a risk-free asset. In the event of default or other credit event, the risk-free asset is redeemed at par and the shorted reference asset is re-purchased at the then current market level and returned to the original owner. The remaining cash (par less the cost of repurchasing the defaulted asset) is then paid to the protection buyer counterparty. Assuming the dealer borrows and shorts the reference security, it must receive a risk-free rate on the proceeds and a default premium sufficient to cover the coupon on the borrowed security. In the American Express example, the breakeven rate is the bid side asset swap rate on the reference security (5.28%) less the default swap premium (42 bp), or 4.86%. At a higher rate the dealer earns positive carry. Note the breakeven risk-free rate is above the general collateral (GC) rate, implying that this is a negative carry transaction. Alternatively, the market maker could use the proceeds of the short sale to pay down its liabilities (effectively investing at its borrowing cost). If the market maker is a highly rated bank the incremental risk is small. But dealers with higher cost of funds must either accept negative carry in this transaction or invest in a more risky asset, such as its own liabilities or commercial paper. Note also if the underlying security could be financed at a special (below GC) rate buyers of protection may be willing to pay a higher default swap premium, resulting in a lower breakeven rate for sellers of protection. Whether favourable financing translates into higher default spread levels will depend of course on the interaction of supply and demand for protection on the credit.

45. To facilitate the comparison we have presented this analysis based on the asset swap spread levels of the cash security. If instead the market maker who sells protection and hedges through borrowing and selling the reference asset is obligated to pay the original owner a fixed coupon, then the floating asset-swapped yield can be swapped to fixed. It can be seen then that pricing of a default swap depends on an interaction of the pricing or spread on the underlying reference asset, the financing rate for the reference asset, and the swap curve. It is also apparent that holding other variables constant, the price of the default swap will change as the credit spread on the underlying cash instrument changes.

46. A good example of how these variables interact is the performance of Brazilian IDU bonds in the 1998-99. During a highly volatile period, default swap spreads tracked asset swap spreads on IDUs. But the differential between these spread series also varied significantly, from near zero in July 1998 (when asset swap spreads were near default swap levels) to as low as a negative 290 bp in November (when asset swaps were substantially less than default swap levels). This variation has been largely a result of changing conditions in the repo market for certain emerging market bonds (including IDUs), which have traded at aggressively special levels at times. The availability of cheap repo market financing for reference securities allowed market makers to increase their bid for protection relative to asset swap spreads. In addition, there are a number of other factors that may lead to differences between observed pricing on a default swap and the pricing implied by this asset swap/repo market framework:

• Liquidity - One problem is that the default swap market may offer limited liquidity. Since credit derivatives are OTC products negotiated separately between individual counterparties, they may be less liquid than the underlying reference credit. This will tend to drive a wedge between the default swap premium and the cash market implied premium and causes the actual premium to be higher than the implied premium. A related problem is that the default swap market tends to be characterised by periods of one-sidedness - i.e., periods when investors either mostly want to buy protection, or to sell protection. Market makers may have difficulty laying off risk in a one-sided market (by entering into an offsetting default swap) or hedging positions if underlying reference assets are not readily available in the cash market. This will result in wider bid/ask spreads, but may also affect the relative level of credit premiums in the cash and default swap markets. Alternatively, sometimes the default swap market may offer more liquidity or ease of transacting than in the underlying cash market, especially in emerging markets and high yield sectors. In these situations, the default swap market plays a role that is in essence similar to the futures market vis-a-vis the underlying government bond market. Just as the futures market provides a liquid medium for investors to express a view about the underlying cash market even though individual cash bond issues may be difficult or expensive to transact, the default swap market allows investors to express a view about a reference entity without having to enter into (in many cases) highly inefficient cash market transactions.

• Correlation - Correlation is primarily an issue at the individual portfolio level, and as such it should not affect the pricing of default swaps per se in reasonably liquid markets. But in a still developing market, correlation problems may give rise to technical supply and demand factors. If correlation in a given portfolio is relatively high or a portfolio has high concentrations that could be highly correlated in certain scenarios, a portfolio manager may be willing to pay a relatively high price (relative to cash market credit premiums) to purchase protection to hedge credit risk. Alternatively a portfolio manager may accept a relatively low premium to sell protection and thereby diversify credit exposure. Over time, however, this activity should actually lead to a more efficient market for default swaps. Using default swaps to manage credit risk in a portfolio context has received much attention in the past year, but to date, most credit portfolio managers are either not actively managing their portfolios in this way or have taken only tentative steps. In many organisations, it has been very difficult to gather the data required to develop robust credit models. As more people and institutions become familiar with quantitative credit techniques and commercially available models become more robust, we expect credit derivatives will be used more widely to manage portfolio credit risk and correlation-related issues. This in turn will enhance market liquidity.

• Counterparty risk - In a credit default swap transaction, the protection buyer has counterparty exposure to the protection seller. If the protection seller and the issuer of the reference credit default simultaneously, the buyer will suffer the full loss despite having paid for default protection. Thus the protection buyer must ensure that the correlation risk between the protection seller and the reference asset is low. In times of low credit concerns (perhaps in periods of high economic growth), buyers of protection will tend not to focus on counterparty risk and A-rated counterparties may be able to sell protection on equivalent terms as AAA-rated counterparties. In periods of high credit concerns, however, buyers of protection might eschew counterparties rated below, say, A1 at any price