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Inflation Indexed Credit Default Swaps

by Marco Avogaro of Bocconi University & Banca IMI, and
Damiano Brigo of Bocconi University & Banca IMI

June 30, 2006

Abstract: The aim of this work is to develop a pricing model for a kind of contract that we term "inflation indexed credit default swaps (IICDS)". IICDS' payoffs are linked to inflation, in that one of the legs of the swap is tied to the inflation rate. In particular, the structure exchanges consumer price index (CPI) growth rate plus a fixed spread minus the relevant libor rate for a protection payment in case of early default of the reference credit. This is inspired by a real market payoff we managed in our work. The method we introduce will be applied to our case but is in fact much more general and may be envisaged in situations involving inflation / credit / interest rate hybrids. The term IICDS itself can be associated to quite different structures. Many variables enter our IICDS valuation. We have the CPI, the nominal and real interest rates, and the default modeling variables. For our pricing purposes we need to choose a way of modeling such variables in a convenient and practical fashion. Our choice 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 (Schönbucher 2004, Brigo 2005) with ideas on Inflation Market Models (Belgrade, Benhamou and Koehler 2004, Mercurio 2005). We discuss numerical methods such as Euler discretization and Monte Carlo simulation for our pricing procedure based on Gaussian and CIR short rate models for rates and default intensity. We analyze the numerical results in details and discuss the impact of correlation between the different rates on the valuation.

JEL Classification: G13.

Keywords: Inflation swap, Credit Default Swap, Inflation CDS, hybrid products, short rate models.

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