CREDIT RISK MODELING USING TIME-CHANGED BROWNIAN MOTION

T. R. Hurd ()
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T. R. Hurd: Department of Mathematics and Statistics, McMaster University, Hamilton ON L8S 4K1, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 08, 1213-1230

Abstract: Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard first passage problem for stochastic processes to capitalize on this time change structure and find that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples. Thus this new notion of first passage can be used to define the time of default in generalized structural credit models. Formulas for defaultable bonds and credit default swaps are given that are both efficiently computable and lead to realistic spread curves. Finally, we show that by treating joint 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 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (13)

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DOI: 10.1142/S0219024909005646

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