To determine which counterparty is most likely to default, we calculate the Distance to Default (DD) using the Merton model formula. The counterparty with the lowest DD is the most likely to default.

Assuming the expected return (drift, $\mu$) is negligible or 0 (since it is not provided), the simplified formula is: $DD = \frac{\ln(V / F) - 0.5 \times \sigma^2 \times T}{\sigma \times \sqrt{T}}$

Where:

• $V$ = Market value of assets
• $F$ = Face value of debt
• $\sigma$ = Annual volatility of assets
• $T$ = Time to maturity = 1 year

Bank A:

• $V/F = 12 / 3 = 4$
• $DD = \frac{\ln(4) - 0.5 \times 0.08^2 \times 1}{0.08 \times \sqrt{1}} = \frac{1.3863 - 0.0032}{0.08} = 17.29$

Bank B:

• $V/F = 8 / 2 = 4$
• $DD = \frac{\ln(4) - 0.5 \times 0.07^2 \times 1}{0.07} = \frac{1.3863 - 0.00245}{0.07} = 19.77$

Bank C:

• $V/F = 45 / 14 = 3.2143$
• $DD = \frac{\ln(3.2143) - 0.5 \times 0.09^2 \times 1}{0.09} = \frac{1.1676 - 0.00405}{0.09} = 12.93$

Bank D:

• $V/F = 32 / 9 = 3.5556$
• $DD = \frac{\ln(3.5556) - 0.5 \times 0.10^2 \times 1}{0.10} = \frac{1.2685 - 0.0050}{0.10} = 12.635$

Bank D has the lowest Distance to Default (12.635), meaning it is the most likely to default among the four counterparties.