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| Credit Risk Modelling Using Time-Changed Brownian Motion by Tom R. Hurd of McMaster University September 18, 2007 Abstract: Motivated by the interplay between structural and reduced form credit models, and in particular the rating class model of Jarrow, Lando and Turnbull, we propose to model the firm value process as a time-changed Brownian motion. We are lead to consider modifying the classic first passage problem for stochastic processes to capitalize on this time change structure. We demonstrate that the distribution functions of such `'first passage times of the second kind'' are efficiently computable in a wide range of useful examples, and thus this notion of first passage can be used to define the time of default in generalized structural credit models. General formulas for credit derivatives are then proven, and shown to be easily computable. Finally, we show that by treating many firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives. Keywords: Credit risk, structural credit model, time change, Lévy process, first passage time, default probability, credit derivative. Books Referenced in this Paper: (what is this?)
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