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Q.3054 The assets of company X are currently worth $1,300,000. In three months the company has to repay $1,000,000 in debt. The expected volatility of the assets is 30% and the expected rate of return on the value of the firm is 15%. What is the probability of default in three months on the basis of the Merton model? Click here to see the standard normal table. | Financial Risk Manager Part 2 Quiz - LeetQuiz

Explanation:

Using Merton formula:

\text{Probability of default} = N\left(\frac{\ln(F) - \ln(V) - \mu(T - t) + 0.5\sigma^2(T - t)}{\sigma\sqrt{T - t}}\right)

Where
σ is the asset value volatility,
N is the probability of the standard normal density function,
F = face value of the bond
V = value of the firm
T = maturity on the bond
μ = expected rate of return

PD = N\left[\frac{\ln 1000,000 - \ln 1,300,000 - 0.15(0.25) + 0.5 \times 0.3^2 \times 0.25}{0.3\sqrt{0.25}}\right] = N(-1.924)

N(-1.92) = 1 - N(1.92) = 1 - 0.9726 = 0.0274

We get the above figure by checking the N value in the normal distribution table.

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