Managing Synthetic CDO Tranches using Base Correlations

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Gaussian Copula Model (con’t) Standard Model Assumptions: One-factor Gaussian copula model F i ( t) = Pr[ τ i < t] ⇔ Φ( Zi ) = F( ti ) Two name example: condition on the market factor Z i = ρ Z + 1− ρε i X 1 ⎧1 = ⎨ ⎩0 prob p ( z) 1 prob (1 − p ( z)) 1 X 2 ⎧1 = ⎨ ⎩0 prob p 2 ( z) prob (1 − p 2 ( z)) Loss Distribution ⎧0 ⎪ l1 L = ⎨ ⎪l2 ⎪ ⎩l1 + l 2 (1 − p ( z))(1 − p p ( z)(1 − p 1 2 p ( z) p 1 1 2 2 1 ( z) 2 ( z)) p ( z)(1 − p ( z)) ( z)) Tranche Pricing Derived from portfolio loss distribution ⎧0 L < a ⎪ L T = ⎨L − a a < L < b ⎪ ⎩b − a b < L Many names … Use FFT (fast Fourier transforms) or recursive method (Andersen, Sidenius, Basu (2003)) to compute probabilities 10
Compound correlations are problematic S<strong>CDO</strong> price is a function of: Asset correlation CDS spreads Maturity Recovery rates Compound correlation: Asset correlation inferred from S<strong>CDO</strong> price Multiple solutions for mezzanine tranches How do you price a tranche with non-standard attachment/detachment points 11
Page 2 and 3: Managing synthetic CDO tranches usi
Page 4 and 5: Synthetic CDO mechanics losses Pro
Page 6 and 7: Protection buyer can hedge by selli
Page 8 and 9: Agenda Synthetic CDO mechanics Ba
Page 12 and 13: Base correlation framework Each tr
Page 14 and 15: Stress tests Base correlations c
Page 16 and 17: Subprime crisis has spread to … L
Page 18 and 19: Stress Test Example for CDX.NA.IG S
Page 20 and 21: So which stress test makes sense I
Page 22 and 23: Agenda Synthetic CDO mechanics Ba
Page 24 and 25: Mapping base correlations between b
Page 26 and 27: Base correlation mapping methods Fi
Page 28 and 29: Method 4: Expected Tranche Loss Pro
Page 30 and 31: Comparison of mappings for iTraxx S
Page 32 and 33: Heterogeneous portfolios Can we fin
Page 34 and 35: Consider linear interpolation iTrax
Page 36: Summary Base correlation are usef

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