A market model on the iTraxx

A market model for the dynamics of credit-risky baskets and indexes such as the iTraxx has long been sought, but because of difficulties with the natural numéraire has remained elusive. Here, Philippe Carpentier proposes using hedging arguments to develop such a model, identifying the resultant dynamics, deriving pricing results and examining the implied correlation

In formulating a market model for credit-risky baskets analogous to the Libor market model (LMM), we must first choose an appropriate numéraire under which the spread is a martingale, then examine what drift is picked up in the pricing measure, and determine a consistent loss process. Inspired by the original work of Brace, Gatarek & Musiela (1997) on the LMM, we can extend to index spreads a proposal by Schönbucher (2004) and Brigo (2005), by taking risky zero-coupon (RZC) bonds as the natural