Credit Risk Models Based on Time Changed Brownian Motion - ICMS

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Difficulties with Black-Cox1 Defaults are predictable, which implies incorrect short timebehaviour;2 The extension to M firms is very difficult: the distribution of firstpassage times for correlated Brownian Motions is basically anunsolvable problem! Zhou (2001) solves it for M = 2, but higherM seems unreachable.3 Rigid structure is hard to fit to real data.Is there another way?Tom Hurd (McMaster) Time Changed Brownian Motion ICMS 2007 6 / 20
Other Approaches1 Reduced form models beginning with Jarrow-Turnbull (1995) haveunpredictable defaults with an exogeneously given instantaneoushazard rate;2 Jarrow-Lando-Turnbull 1997 model the credit rating as a Markovchain with stochastic transition probabilities. This modelinterpolates between structural and reduced form frameworks.3 Lando (1998), Arvanitis-Gregory-Laurent (1999), Hurd-Kuznetsov(2007) give computationally efficient versions of JLT.4 Carr-Wu (2005) give reduced form models with the hazard ratetied to the level of the stock price.Tom Hurd (McMaster) Time Changed Brownian Motion ICMS 2007 7 / 20
Page 1 and 2: Credit Ris
Page 3 and 4: Toronto: the place to be in 2010 !W
Page 9 and 10: Two outstanding issues in credit ri
Page 11: Black-Cox (1976)A time-consistent m
Page 15 and 16: Jump-Diffusion Default Mode
Page 17 and 18: First passage times for time-change
Page 19 and 20: Example1 Take L0 = 1;2 Take b = 0.0
Page 21 and 22: NumericsYield Spread0.35$L 0=0.3$0.
Page 23 and 24: Computing the Joint Default Distrib
Page 25 and 26: Risk Neutral Dynam
Page 31 and 32: Equity-Credit Comp
Page 33 and 34: Conclusion1 By taking Lt = X Gt wit

Credit Risk Models Based on Time Changed Brownian Motion - ICMS

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