Credit Risk Models Based on Time Changed Brownian Motion - ICMS

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A sample path of Lévy time change G t43.532.521.510.500 0.5 1 1.5 2 2.5 3 3.5 4Tom Hurd (McMaster) Time Changed Brownian Motion ICMS 2007 10 / 20
First passage times for time-changed BM1 The usual extension of the Black-Cox model would be to definedefault time to be the first passage time:t (1) = inf{t|L t ≤ 0}2 This has been well studied, and is difficult to compute!3 Here is an alternative:t (2) = inf{t|G t ≥ t ∗ }wheret ∗ = inf{t|X t ≤ 0}4 This is relatively easy to compute.5 The natural stopped process is L(2)t := X Gt∧t ∗.Tom Hurd (McMaster) Time Changed Brownian Motion ICMS 2007 11 / 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 and 12: Black-Cox (1976)A time-consistent m
Page 13 and 14: Other Approaches1 Reduced form mode
Page 15: Jump-Diffusion Default Mode
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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