Explanation:
Using the Merton model, a firm's likelihood of defaulting is evaluated using the Distance to Default (DD). The simplified distance to default can be calculated as: DD = [ln(V / F) + (μ - σ² / 2) * T] / (σ * √T)
Assuming the expected return (μ) is negligible or zero, and T = 1 year, we primarily evaluate ln(V / F) / σ:
Bank D has the lowest distance to default (12.68). A lower distance to default indicates that the counterparty's asset value is closer to the default threshold (face value of debt), making Bank D the most likely to default.
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Q.54 ABC Bank’s credit manager is using the Merton model and the distance to default formula to monitor his bank’s counterparties to valuation and financial conditions changes. The manager has gathered the following information on the counterparties.
| Bank A | Bank B | Bank C | Bank D | |
|---|---|---|---|---|
| Market value of assets | $12m | $8m | $45m | $32m |
| Face value of debt | $3m | $2 | $14 | $9 |
| Market value of debt | $2.5m | $1.5m | $14m | $8m |
| Annual volatility of assets | 8% | 7% | 9% | 10% |
If counterparties’ debt is a zero-coupon bond maturing in 1 year, is their only liability for each counterparty, which counterparty is most likely to default?
A
Bank A
B
Bank B
C
Bank C
D
Bank D
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