NO.PZ2023040701000113
问题如下：
FIQ Bank is a highly rated corporate and institutional bank that operates a client facing credit default swap (CDS) desk. Larry Eckle is a CDS client strategist. Mark Priore is FIQ’s chief CDS trader. Eckle and Priore are meeting with Brian Bregen, a portfolio manager for BLB Fund, to discuss investment and trading strategies for bonds, CDSs, and equities.
Bregen begins the discussion by asking for a refresher on basic CDS concepts and parameters. Eckle replies that a CDS includes both a premium leg and a payment leg and that expected loss is among the functions that affect its price. Eckle provides information for a bond issued by Apollo Company.
Exhibit 1 Information for Apollo Bond
Based on the information in Exhibit 1, the expected loss for Apollo bond is likely closest to:
选项：
A.$35.28.
$48.03.
$90.00.
解释：
Correct Answer: B
Expected loss = Summation of probability of default × Loss given default for each discrete cash flow, as illustrated
Calculation:
Cash flow (CF):
$50.00 interest coupons, $1,000.00 principal repayment
Expected loss (EL)
= CF × Conditional probability of default (PD) × Loss given default (LGD),
where LGD = 1 – Recovery rate
Conditional
probability of default:
Year 1 PD = 2.0% =
2% Hazard rate
[98% no default in
Year 1 (100% – 2% PD)].
Year 2 PD = 4.45%
= 2.0% (Y1) + 2.45% (Y2)
[(2.5% Hazard rate
× 98% No default Y1); 95.50% no default in Year 2 (100% – 4.5% PD)].
Year 3 PD = 7.317%
= 2.0% (Y1) + 2.45% (Y2) + 2.867% (Y3)
[(3.0% Hazard rate
× 0.955 No default Y2); 92.684% no default in Year 3 (100% – 7.317%PD)].
Expected loss =
$48.03, where
Year 1 = $50.00 CF
× (2.00% Y1 PD × 0.60 LGD) = $0.60.
Year 2 = $50.00 CF
× (4.45% Y2 PD × 0.60 LGD) = $1.34.
Year 3 = $1,050.00
CF × (7.316% Y3 PD × 0.60 LGD) = $46.09.
A is incorrect. An
expected loss of $35.28 incorrectly presumes an equivalent hazard rate of 2%
for each year:
1 Probability of
survival represents the probability of no default: 0.98 × 0.98 ×0.98 = 0.94119.
2 Probability of
default: 1.0 – Probability of survival = 1 – 0.94119 = 0.058810 = 5.8810%.
3 Expected loss =
Probability of default × Loss given default × Face amount = 5.8810% × 60% ×
$1,000 = $35.28.
C is incorrect. An expected loss of $90.00 is incorrectly determined by the following calculation: $1,000 (face amount of the bond) × 15.00% (summation of the three years of 5.00% interest coupons) × (1.0 – 0.40 Recovery rate).
我算
第一年违约：2%
第二年违约：98%*2.5%
第三年违约：98%*97.5%*3%
这三个年头不管哪个年头违约，损失都是1050*60%
我相当于穷举了所有破产的可能性并且加在一起求期望，
所以最后的结果就是（2%+98%*2.5%+98%*97.5%*3%）*1050*60%=46.09，请问这个逻辑错误在哪。
