Credit derivatives pricing

The reduced form models described earlier models are a new generation of credit derivative pricing models, which are now increasingly being used to price total return swaps. 

Reduced Form Kamakura implements reduced form models from the Robert Jarrow family, such as the Jarrow-Chava version. These models use equity, debt, and credit derivative prices. 

In addition, Kamakura s research has shown that reduced form models utilizing credit derivatives prices are the most effective default predictor ... 

Our results indicate that reduced form models based on credit derivatives prices and bond prices have the best performance from both a statistical and a practical point of view, said Profes-... 

Credit-derivative pricing is similar to the pricing of other off-balance-sheet products, such as equity, currency, and bond derivatives. The main difference is that the latter can be priced and hedged with reference to the underlying asset, and credit derivatives cannot. The pricing model for credit products incorporates statistical data concerning the likelihood of default, the probability of payout, and market level of risk tolerance. 

If this difference is positive we have a positive basis, and it happens when credit derivates trade at higher prices than asset swaps. Otherwise, if the difference is negative we have a negative basis. Consider the following example of a positive basis trade for HERIM and TKAAV. For both bonds, we calculate the CDS spread which is equal to 86.3 for HERIM and equal to 88.6 for TKAAV. The CDS basis over the ASW spread determined before is equal to 46.8 for HERIM and equal to 49.5 for TKAAV. However, the basis illustrated in Figure 1.6 is different because CRVD measures them relative to the Z-spread, which is 50.7 for HERIM and 48 for TKAAV. The basis relative to the Z-spread is equal to 35.6 for HERIM and 40.6 for TKAAV. So, we note that either the ASW spread or the Z-spread can be used as the basis performance, giving a similar result and positive basis in both cases. 

Central banks and market practitioners use interest rates prevailing in the government bond market to extract certain information, the most important of which is implied forward rates. These are an estimate of the market s expectations about the future directirMi of short-term interest rates. They are important because they signify the market s expectafirMis about the future path of interest rates however, they are also used in derivative pricing and to create synthetic bond prices from the extent of credit spreads of corporate bonds. 

In this chapter we introduce the main types of credit derivatives, and describe their nses and applications. We also introduce concepts in pricing and valuation of these instruments. 

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. 

Asset swaps are used to alter the cash flow profile of a bond. The asset swap market is an important segment of the credit derivatives market since it explicitly sets out the price of credit as a spread over LIBOR. Pricing a bond by reference to LIBOR is commonly used and the spread over LIBOR is a measure of credit risk in the cash flow of the underlying... 

Pricing models for credit derivatives fall into two classes ... 

Merton applied option pricing techniques to the valuation of corporate debt." By extension the pricing of credit derivatives based on corporate debt may in some circumstances be treated as an option on debt, which is therefore analogous to an option on an option model. 

Reduced form models are a form of no-arbitrage model. These models can be fitted to the current term structure of risky bonds to generate no arbitrage prices. In this way the pricing of credit derivatives using these models will be consistent with the market data on the credit risky bonds traded in the market. These models allow the default process to be separated from the asset value and are more commonly used to price credit derivatives. 

The statistical transition matrix is adjusted by calibrating the expected risky bond values to the market values for risky bonds. The adjusted matrix is referred to as the risk-neutral transition matrix. The risk-neutral transition matrix is key to the pricing of several credit derivatives. 

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 derivatives that pay out according to the level of the credit spread would require that the credit spread process is adequately modeled. In order to achieve this, a stochastic process for the distribution of outcomes for the credit spread is an important consideration. 

In practice, the spread information from the CDS market is used to imply the probability of default and the hazard rate for the underlying reference entity. The recovery rate is an input when the calculation of implied probabilities takes place. It is common to assume a recovery rate that reflects the rate on the cheapest to deliver deliverable obligation. Credit derivative traders will monitor the prices of the cheapest to deliver bonds (i.e., deliverable obligations with the lowest recovery), when constructing hedges. 

This section examines a few commercially available software packages and analytic tools designed to mitigate risk in the increasingly innovative credit derivative market. It reviews CDS data providers, examines analytic programs designed to provide expected default probabilities and theoretical prices, and highlights applications intended to simplify CDO investments. ... 

Creditex, a market-supported interdealer credit derivative broker, offers PriceTracker as a tool for accessing and monitoring CDS prices. Users have complete access to all of the live prices collected through the interdealer brokerage business. 

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. 

The products discussed include interest rate swaps, options, and credit derivatives. There is also a chapter on the theory behind forward and fiimres pricing, with a case smdy featuring the price history and implied repo rate for the CBOT long bond future. 

Banks employ a number of methods to price credit derivatives. This section presents a quick overview. Readers wishing a more in-depth discussion should consult the references listed for this chapter in the References... 

For more detail on modeling credit spreads to price credit derivatives, see Choudhry (2004). 

Das, S. 1997. Credit Derivatives Products, Applications and Pricing Singapore John Wiley Sons. 

The other major use by banks of credit derivatives is as a product offering for clients. The CDS market has developed exactly as the market did in interest rate swaps, with banks offering two-way prices... 

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