Problem 2 Consider two credits D1 and D2. Assume that the survival ofthe credit :1 is dependent on a latent variable Ai~N(O, 1). Specifically, a default occurs before time T if the value of A; is less than a time dependent threshold C1-(T) i.e., Per.- 3 T) = P(Ai s (rim) 2 1 (3.0") Here, (Qt-(T) is the time Tsurvival probability of credit 1' implied by the CDS market. Consider the Aiziz'l' llizgi where Z~N(0, 1) is the market factor and i~N(0, 1) are the idiosyncratic factors specific to following onefactor model: 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 D1 defaults at future time I1 and it has a nonzero asset correlation with D2, then we would expect this default to have an impact on the conditional default probability of D2. We denote the default time for credit B as 12 and the correlation between credits as p. a) Calculate Q2(t, T) the forward survival curve for a credit 02 conditional on default of credit D1 at time t and compare 62 (t, T) with Q2(t, T) the unconditional forward survival curve. Please comment on the relationship