36 answers 1 b the yield spread is the singlepoint

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36Answers:1. B.The yield spread is the "single­point" difference between the yield to maturity (YTM)and the corresponding riskless spot rate; in this case, yield spread ~= 4.0% ­ 1.61% ~=2.39%. As the endpoints at year 2.0 are near to each other, this yield is only slightly lessthan the z­spread of 2.42%, due primarily to the fact that the upper blue line endpoint mustnecessarily be slightly greater than the 4.0% YTM. If the corresponding riskless swap rate isnecessarily interpolated, then this yield spread is an i­spread.In regard to (A), (C), and (D), each are TRUE.2. C. \$151.16We shock the z­spread by one basis point, from 3.00% to 2.99%:\$5.00*exp[­(1.0%+2.99%)*0.5] + \$5.00*exp[­(2.0%+2.99%)*1.5] + \$105.00*exp[­(3.0%+2.99%)*1.5] = \$105.6350,which is a price increase of about \$0.01512 and per \$1.0 million of par = \$0.01512 *1,000,000/100 = \$151.162.Note, per Malz, we can be more precise by shocking + 0.5 basis point and ­ 0.5 basis point,but the result is nearby at \$151.15 (due to convexity, including the up­yield shock implies aslightly lower DVCS if we are more precise)3. C. 39.35%Lambda = 6 defaults/1 year = 0.5 defaults per month.The "waiting time" probability is characterized by the exponential distribution:P[next default within one month] = 1 ­ EXP(­lambda*T), where T =1 is given by 1 ­ EXP(­0.5*1) = 1 ­ EXP(­0.5) = 39.35%P[no default within one next month] = EXP(­lambda*T) = EXP(­0.5*1) = EXP(­0.5) = 60.65%Note equivalently, we can view lambda as 6 defaults per year, with T = 1/12, such that:P[next default within one month] = 1 ­ EXP(­6*1/12).4. D.The conditional one­year PD is equal to 8.6%, same as the unconditional one­yeardefault probability, and near to the hazard rate (9.0%) since the hazard rate is aninstantaneous conditional PD.To paraphrase Malz: the difference between the two­ and one­year default probabilities—theprobability of the joint event of survival through the first year and default in the second—is7.87%.The conditional one­year default probability, given survival through the first year, is thedifference between the two probabilities (7.87%), divided by the one­year survival probabilityof exp(­9.0%*1) = 91.39% = 1 ­ 8.61%. So the conditional one­year PD = 7.87%/(1­8.61%) =8.61%, which in this example is equal to the unconditional one­year default probability.In regard to (A), (B) and (C), each are TRUE.In regard to (A), the unconditional one­year default probability = 1 ­ exp(­9.0%*1) =8.61%.In regard to (B), the unconditional two­year default probability = 1 ­ exp(­9.0%*2) =16.47%.In regard to (C), the probability of joint event of survival through the first year anddefault in the second year = 16.47% ­ 8.61% = 7.87%.
375. C.The term highlighted in BLUE models the payment of the accrued premium (payable bythe protection) in the event of default under an assumption of default midway through thequarter.Malz: "In the event of default, the protection buyer must pay the portion of the spreadpremium that accrued between the time of the last quarterly payment and the default date ...

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Term
Winter
Professor
NoProfessor
Tags
Subprime mortgage crisis, Subprime lending, Credit default swap