
Explanation:
To compute the expected loss, the outstanding balance has to be multiplied with the product of PD, EAD and LGD.
The probability of default can be calculated using the following formula:
Where:
N = Cumulative normal distribution
F = face value of zero-coupon bond
V = value of the firm
T = time to maturity
σ = volatility of the firm's value
Note that we have not been provided the values for F and V but their ratio has been provided.
, therefore, .
The expression can also be written as .
Hence:
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Q.3193 A firm’s return for the next five years is expected to be 15% and the volatility of the firm’s value is 19%. The firm has issued a zero-coupon bond which will mature in 5 years. The value of the firm is 1.1 times the face value of the bond and the current interest rate is 7.5%. Using the Merton Model, compute the default probability if LGD is 75% and EAD is 100%. Assume the value of the bond is x.
A
2.832%
B
3.776%
C
7.202%
D
1.037%