Financial Risk Manager Part 2

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Explanation:

PD = N\left[\frac{\ln(F) - \ln(V_A) - \mu T + \frac{1}{2}\sigma_A^2 \times T}{\sigma_A \sqrt{T}}\right]

From the question, we have:
$F = \`$ 478$ million, $V_A = \ $280`$ million, $T = 7$ , $\sigma_A = 0.21$ , $\mu = 0.18$
$N$ is the cumulative normal distribution operator. Therefore:

PD = N\left[\frac{\ln(478) - \ln(280) - 7 \times 0.18 + 0.5 \times 0.21^2 \times 7}{0.21 \times \sqrt{7}}\right]

= N(-1.0274)

= 1 - N(1.0274)

= 0.1515

Explanation:

PD = N\left[\frac{\ln(F) - \ln(V_A) - \mu T + \frac{1}{2}\sigma_A^2 \times T}{\sigma_A \sqrt{T}}\right]

From the question, we have:
$F = \`$ 478$ million, $V_A = \ $280`$ million, $T = 7$ , $\sigma_A = 0.21$ , $\mu = 0.18$
$N$ is the cumulative normal distribution operator. Therefore:

PD = N\left[\frac{\ln(478) - \ln(280) - 7 \times 0.18 + 0.5 \times 0.21^2 \times 7}{0.21 \times \sqrt{7}}\right]

= N(-1.0274)

= 1 - N(1.0274)

= 0.1515

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Q.2876 Suppose that Logos International Company has an asset value of `$280` million and was issued a loan by Broadways Bank. The loan has 7 years remaining to reach maturity. We are also informed that the face value of the debt is `$478` million. The risk expected return is 18% and the instantaneous assets value volatility is 21%. Compute the value of default probability following the Merton approach and applying the Black Scholes Merton Formula.

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Last updated: July 5, 2026 at 07:27

0.898

0.217

0.1515

0.055