The aim of this work is to develop a pricing model for a recent type of credit derivative contracts. Such contracts have their payoffs linked to some current rate of inflation. This is to say they have a particular floating-to-floating interest rate structure in which one of the floating legs is tied to the inflation rate. Meanwhile, being these credit derivatives, their whole contingent claim depends on the credit worthiness of a third party. We will generally name contracts of this kind "Inflation Indexed Credit Default Swaps" or IICDS.
It will be clear that these contracts find their economic sense when two (or more) parties agree on the following assumptions in interpreting the market: the protection seller believes that the spread between inflation and nominal interest rates will rise but thinks this will not affect the overall economic situation and that the credit quality of the contractual underlying economic agent will not change substantially whilst the protection buyer thinks inflation will rise and that this may deteriorate the creditworthiness of economic agents and of the underlying in particular. Usually the buyer of such contracts has opened positions with one or more of such economic agents and fears the possibility of a credit event affecting his wealth or current income.
Many variables enter the inflation indexed credit default swap payoffs. We have the Consumer Price Index (CPI), the nominal and real interest rates, and the default modeling variables. For our pricing purposes we needed to choose a way of modeling such variables in a convenient and practical fashion. The choice of the best suited "technology" fell on the familiar short rate model setting, although frameworks based on recent market models for credit and inflation could be attempted in principle, for example by combining ideas on Credit Default Swap Market Models (Schonbucher 2004, Brigo 2005) with ideas on Inflation Market Models (Benhamou 2004, Mercurio 2005).
Contents
1 Introduction
2 An Overview of In ation Modeling
2.1 Inflation
2.2 Inflation Modeling: General Framework
2.3 Zero Coupon and Year-on-Year Inflation-Indexed Swaps
2.4 A short guide to the Hull-White interest rate model
2.5 The Jarrow-Yildirim model
2.6 Pricing with the Jarrow-Yildirim/Hull-White model
- 2.6.1 Pricing of Year-on-year Inflation Indexed Swaps
2.6.2 Pricing of Inflation Indexed Caps and Floors
3 Introduction to credit risk
3.1 A brief overview on credit default swaps
3.2 Modeling the default time
3.3 A brief introduction to the Cox-Ingersoll-Ross model for the intensity of default
4 In ation-Indexed CDS pricing model
4.1 Defining the contractual payoff
4.2 Pricing
- 4.2.1 Pricing IICDS when the intensity of default is independent from interest rates and the CPI
4.2.2 Pricing IICDS when the intensity of default is correlated with interest rates and the CPI
4.2.3 Pricing the IICDS
4.2.4 Pricing the IICDS with several correlation patterns
4.2.5 Pricing the IICDS with higher volatility levels
5 Conclusions
