Credit default swaps pricing

The cash flows of a typical credit default swap are set out in Exhibit 21.1. Exhibit 21.2 shows the Bloomberg screen CDS for credit default swap prices. 

Return from a holding of fixed-income securities may be measured in more than one way. The most common approach is to consider the asset-swap spread. More sophisticated investors also consider the basis spread between the cash bond and the same-name credit default swap price, which is known as the basis. In this chapter we consider the most accessible way to measure bond return. 

A credit default swap (CDS) price provides fundamental credit risk information of a specific reference entity or asset. As explained before, asset swaps are used to transform the cash flows of a corporate bond for interest rate hedging purpose. Since the asset swaps are priced at a spread over the interbank rate, the ASW spread is the credit risk of the same one. However, market evidence shows that credit default swaps trade at a different level to asset swaps due to technical... 

EXHIBIT 21.2 Credit Default Swap Bloomberg Price Screen... 

An interesting development in the credit default swap market is the response of protection sellers to credit events, the impact is ultimately reflected in the price of credit default swaps, as reflected by the credit default swap spread. Credit derivative markets have experienced spread widening at times of bad credit related news, in effect this reflects the protection sellers pricing the risk of the additional probability of a credit event into the protection they sell. 

Since credit default swaps are written on the reference entities, their pricing provide information on the default probabilities of the issuer and are not subject to liquidity premia that can be present in the credit spreads of the credit risky bonds. Therefore, the term structure of credit default swap spreads for a particular issuer is used to determine the cumulative default probability of the issuer. 

Various credit derivatives may be priced using this model for example, credit default swaps, total return swaps, and credit spread options. The pricing of these products requires the generation of the appropriate credit dependent cash flows at each node on a lattice of possible outcomes. The fair value may be determined by discounting the probability-weighted cash flows. The probability of the outcomes would be determined by reference to the risk neutral transition matrix. 

The pricing of credit default swaps is determined in the credit default swap market by traders who determine the credit default swap spread through their assessment of the default risk of the reference obligations. This spread information can give valuable information about the key pricing components of the reference credit implied probability of default of the reference credit and recovery assumptions. These price... 

This last equation shows the direct relationship between the probability of default and the market credit default swap quotes. Therefore, using equation (21.14) and the term structure of credit, we may be able to boot-strap the market implied probability of default from the credit curves, which are in effect the range of credit default swap quotes by maturity. Equation (21.14) is only approximate because in practice we would need to ensure that the timing of projected cash flows are accurately reflected in the pricing model. For example, the actual payment on the contingent leg may depend on the settlement date for the swap. 

Recovery rates on bonds vary by the position in the reference entity s capital structure and the level of security offered to the bond holders. Determining the appropriate recovery rate is not a trivial process and requires careful analysis into the traded prices of deliverable obligations for the reference credit. In practice there is limited historical information on the recovery rates experienced for credit default swaps. 

In this way, any changes of shape and perceptions of the premium for CDS protection are reflected in the spreads observed in the market. In periods of extreme price volatility, as seen in the middle of 2002, the curves may invert to reflect the fact that the cost of protection for shorter-dated protection trades at wider levels than the longer-dated protection. This is consistent with the pricing theory for credit default swaps. 

See Moorad Choudhry, Issues in the Asset Swap Pricing of Credit Default Swaps, in Frank J. Fabozzi (editor), Professional Perspectives on Fixed Income Portfolio Management Volume 4 (Hoboken, NJ John Wiley Sons, Inc., 2003). 

In recent years, the valnation of certain synthetic instrnments, snch as credit default swaps (CDS), has become a routine task in financial markets. Meanwhile, variations on the core CDS product are emerging, and more complex instruments, such as synthetic collateralized debt obligations (CDOs), that use CDSs as building blocks for larger transactions continue to see analytic evolution. This chapter provides an introduction to the basics of pricing and explores some of the tools available to those involved in the synthetics market. 

The Pricing of Credit Default Swaps and Synthetic Collateralized Debt Obligations... 

Although the pricing of a credit default swap can be numerically reduced to a model, the inputs to that model still remain subjective. How can one calculate an exact valne for R, the recovery value of an issuer s assets post-default Or, more importantly, how can one calculate the hazard rate X for an issuer What is the probability that a particular issuer will default in five years Determining the true credit risk of an issuer has been a topic of intense focus in recent years and, as a result, quite a variety of methods and models have surfaced. 

The NX CR Engine is a pricing and risk management tool that allows users to model a wide range of credit derivative products. It produces theoretical prices for single-name credit default swaps, baskets and CDOs. In addition, NumeriX s software produces survival probabilities, recovery rates and correlations. 

Asset-swap pricing is commonly applied to credit-default swaps, especially by risk management departments seeking to price the transactions held on credit traders book. A par asset swap typically combines an interest rate swap with the sale of an asset, such as a fixed-rate corporate bond, at par and with no interest accrued. The coupon on the bond is paid in return for LIBOR plus, if necessary, a spread, known as the asset-swap spread. This spread is the price of the asset swap. It is a function of the credit risk of the underlying asset. That makes it suitable as the basis for the price payable on a credit default swap written on that asset. 

If a credit event occurs, the SPV usually pays out a cash amount equal to the par value of the underlying assets covered by the credit default swap, less their post-default price. Less commonly, the SPV physically settles the credit-default swap by purchasing the defaulted assets at par value. The credit loss is then passed on to the investors according to the priority of the tranches they hold. 

A Z-spread can be calculated relative to any benchmark spot rate curve in the same manner. The question arises what does the Z-spread mean when the benchmark is not the euro benchmark spot rate curve (i.e., default-free spot rate curve) This is especially true in Europe where swaps curves are commonly used as a benchmark for pricing. When the government spot rate curve is the benchmark, we indicated that the Z-spread for nongovernment issues captured credit risk, liquidity risk, and any option risks. When the benchmark is the spot rate curve for the issuer, for example, the Z-spread reflects the spread attributable to the issue s liquidity risk and any option risks. Accordingly, when a Z-spread is cited, it must be cited relative to some benchmark spot rate curve. This is essential because it indicates the credit and sector risks that are being considered when the Z-spread is calculated. Vendors of analytical systems such Bloomberg commonly allow the user to select a benchmark. 

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