Tom Hurd (McMaster University, Canada)

We begin by reviewing some classic problems in finance that boil down to a problem of first passage of an underlying stochastic process. Although jump diffusions are widely used for modeling financial time series, they have been only slowly adopted in
some areas, like credit risk, perhaps because of the intractable nature of their first passage problem. In this talk I show how this difficulty can be circumvented. Thus freed, we are able to investigate some consequences of adding jumps to structural credit models
for one firm. As an example of what can be done, a class of credit-equity hybrid models is proposed. At the end of the talk, we will move to multivariate credit models and briefly consider the implications of introducing dynamic default correlations through time change.