## Question

###### Consider two credits D1 and Dz Assume that the survival of the credit is dependent on a latent variable A;~N(O, 1). Specifically, a default occurs before time Tif the value of A; is less than a time dependent threshold C; (T) ie-,P(t <T) = P(A; < C(T)) =1-Q (t)Here, Q;(T) is the time T survival probability of credit implied by the CDS market: Consider the following _ one-factor model:Ai = B+z + I1 - Bzewhere Z~N(O,1) is the market factor and &~N(O,1) are the idiosyncratic factors spec

Consider two credits D1 and Dz Assume that the survival of the credit is dependent on a latent variable A;~N(O, 1). Specifically, a default occurs before time Tif the value of A; is less than a time dependent threshold C; (T) ie-, P(t <T) = P(A; < C(T)) =1-Q (t) Here, Q;(T) is the time T survival probability of credit implied by the CDS market: Consider the following _ one-factor model: Ai = B+z + I1 - Bze where Z~N(O,1) is the market factor and &~N(O,1) are the idiosyncratic factors specific to each credit: Within this framework; there are no explicit = spread dynamics. The only events that we can observe are the defaults of credits_ A credit can have spread dynamics when we condition on the default and survival behavior of the other credits to which this credit is correlated, .If Di defaults at future time T1 and it has non-zero asset correlation with Dz, then we would expect this default to have an impact on the conditional default probability of Dz. We denote the default time for credit B as Tz and the correlation between credits as p Calculate Q2(t,T) the forward survival curve for a credit Dz conditional on default of credit Di at time and compare Qz(t,T) with Qz(t,T) the unconditional forward survival curve_ Please comment on the relationship. Assume that the initial CDS spread for credit D is flat at 60 bps, the CDS spread for credit Dz is flat at 120 bps and the recovery rate is R = 40% for both credits. Calculate the forward spread curve of credit Dz conditional on default of credit D at time t e(0,5). Plot the calculated forward spreads for correlation between assets P â‚¬ {-0.5,-0.25,0,0.25,0.5}. Discuss the relationship between the conditional spread curve of credit Dz and the asset correlation p_