Abstract and Keywords
This article gives an introduction to the mechanics and techniques used to develop market models for credit, focusing on the single credit case. The concept of a background filtration was introduced by Jeanblanc and Rutkowski (2000), and has been used by multiple authors since, e.g., Jamshidian (2004) and Brigo and Morini (2005). The theory is worked out in relative detail in Section 2, which also formalises the concept of a background price process. Section 3 shows how this theory can be used to derive Black-type pricing formulas for default swaptions. A full market model is developed in Section 4. It turns out that, in the case where both credit spreads and interest rates are stochastic and dependent, the situation is not as clean as for interest rate market models. This is because default protection payoffs inherently contain a measure mismatch due to the timing of default and the payout. In the case where credit and interest rates are independent, the situation simplifies considerably. Under these simplifications, Section 5 describes in detail the induction steps needed to construct a market model from scratch. Section 6 describes an alternative method of constructing credit default swaps (CDS) market models. Instead of using forward default intensities as model primitives, it directly describes the dynamics of certain survival probability ratios. Finally, the pricing of constant maturity CDS contracts is examined in Section 7.
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