On modelling credit risk using Arbitrage Free Models

By examining the distribution of state prices obtained from binomial versions of Jarrow and Turnbull (1995), Lando (1998) and Duffie and Singleton (1999), we are able to suggest which credit risk parameters are of critical interest. We find that it appears worthwhile to parameterize credit risk since even the simplest parameterized model obtains large changes in the distribution of state prices when compared to a non-parameterized model. Similarly we find large differences in the distribution of state prices as we add correlation and moderate changes as we add time varying recovery rates. Finally, the choice between the RM or RF recovery assumption appears innocuous, but the choice between RT and these two recovery assumptions is not.