BasketCDSPres

BasketCDSPres - Structural Models of Credit Spectral...

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Unformatted text preview: Structural Models of Credit Spectral Element Methods Structural Models of Credit: A spectral Element Approach. Pierre Garreau Financial Mathematics Seminar Florida State University November 17, 2011 Structural Models of Credit Spectral Element Methods 2 3 4 5 6 7 8 9 10 01/01/05 01/01/06 01/01/07 01/01/08 01/01/09 01/01/10 01/01/11 01/01/12 Baa Aaa 20Y TBill Figure: 20-Year Aaa and Baa bond spreads. Structural Models of Credit Spectral Element Methods Definition A credit spread is the premium paid to insure the risk of default of the underlying entity, i.e. it is the difference between the risk free rate, r t , and the yield on the corporate bond, y t . B t = e- r t t D t = Le- y t t s t = ln D t / LB t t Structural Models of Credit Spectral Element Methods 1 2 3 4 5 6 08/13 08/27 09/10 09/24 10/08 10/22 11/05 11/19 MF Global Figure: MF Global stock price. Structural Models of Credit Spectral Element Methods Asset Liabilities V t S t D t Table: Modigliani-Miller theorem Structural Models of Credit Spectral Element Methods t s t s t s t s t (1 R ) t = 0 t N = T . . . Structural Models of Credit Spectral Element Methods DL = E bracketleftBig (1 R )1 < T e- integraltext r s ds bracketrightBig t s t s t s t s t (1 R ) t = 0 t N = T . . . FL = E bracketleftBigg N summationdisplay i =1 s t 1 > t i e- integraltext t i r s ds bracketrightBigg Structural Models of Credit Spectral Element Methods DL = (1 R ) integraldisplay T B (0 , s ) d P ( s ) t s t s t s t s t (1 R ) t = 0 t N = T . . . FL = N summationdisplay i =1 s t P ( > t i ) B (0 , t i ) Structural Models of Credit Spectral Element Methods DL = (1 R ) parenleftBigg 1 e- rT P ( > T ) r integraldisplay T P ( > s ) e- rs ds parenrightBigg t s t s t s t s t (1 R ) t = 0 t N = T . . . FL = N summationdisplay i =1 s t P ( > t i ) e- rt i Structural Models of Credit Spectral Element Methods s = (1 R ) parenleftBig 1 e- rT P ( > T ) r integraltext T P ( > s ) e- rs ds parenrightBig N i =1 t P ( > t i ) e- rt i Structural Models of Credit Spectral Element Methods Default time = inf { t : min s t V s D } P ( > t ) = P (min s t V s > D ) = E bracketleftbig 1 min s t V s > D bracketrightbig D T = R T . 1 { T } + D . 1 { > T } 4 6 8 10 12 14 16 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Figure: V t = V e t + Wt + N t i =0 Y i Structural Models of Credit Spectral Element Methods Default time = T . 1 { V T D } + 1 { V T > D } P ( > T ) = P ( V T > D ) D T = V T . 1 { V T...
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This note was uploaded on 01/15/2012 for the course MAT 5939 taught by Professor Garreau during the Fall '11 term at FSU.

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BasketCDSPres - Structural Models of Credit Spectral...

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