Credit Risk Models Based on Time Changed Brownian Motion - ICMS
Credit Risk Models Based on Time Changed Brownian Motion - ICMS
Credit Risk Models Based on Time Changed Brownian Motion - ICMS
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A Simple Multifirm Model1 Take independent drifting BMs {X 1 , X 2 , . . . , X M }, andparameters {x i , β i }2 Subject them to the same time-change Gt :L i (t) = X i G t3 Moments:Mean = E[L i t] = x i + β i tE[G 1 ]/2Variance = Var[L i t] = t(E[G 1 ] + (β i ) 2 Var[G 1 ])Correlati<strong>on</strong> ρ ij =(1 + E[G(1)] ) () −1/2 −1/2βi 2Var[G(1)] 1 + E[G(1)]βj 2Var[G(1)] Tom Hurd (McMaster) <strong>Time</strong> <strong>Changed</strong> <strong>Brownian</strong> Moti<strong>on</strong> <strong>ICMS</strong> 2007 16 / 20
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