Explanation:
EL = EA × PD × LR
Exposure at default,
EA = drawn amount + drawdown on default
= 80% × 100,000 + 70% × (100,000 − 80% × 100,000)
= 80,000 + 14,000 = 94,000
PD = 2%
LR = 40%
Thus,
EL = 94,000 × 0.02 × 0.4 = USD 752
UL = EA × √(PD × σ²_LR + LR² × σ²_PD)
σ²_LR = 0.3²
σ²_PD = 0.14² = 0.0196
Thus,
UL = 94,000 × √(0.02 × 0.3² + 0.4² × 0.0196)
= USD 6,604
Ultimate access to all questions.
Q.3683 A bank has booked a loan with a total commitment amounting to $100,000. 80% of this amount is currently outstanding. The default probability of the loan is assumed to be 2% for the next year, and the loss-given default (LGD) stands at 40%. The standard deviation of LGD is 30%, and the standard deviation of the probability of default is 14%. Drawdown on default (i.e., the fraction of the undrawn loan) is assumed to be 70%. Determine the expected and unexpected losses for the bank.
A
Expected loss = USD 640, unexpected loss = USD 5,621
B
Expected loss = USD 640, unexpected loss = USD 6,604
C
Expected loss = USD 752, unexpected loss = USD 6,604
D
Expected loss = USD 752, unexpected loss = USD 5,621
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