Financial Risk Manager Part 2

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Explanation:

In the Merton model, the parameters $d_1$ and $d_2$ are related by the formula: $d_2 = d_1 - \sigma_V \sqrt{T}$

Where:

$d_1 = 3.217790$
$d_2 = 3.038905$
$T = 5 \text{ years}$
$\sigma_V$ is the firm value volatility.

Rearranging the formula to solve for $\sigma_V$ : $\sigma_V = \frac{d_1 - d_2}{\sqrt{T}}$ $\sigma_V = \frac{3.217790 - 3.038905}{\sqrt{5}}$ $\sigma_V = \frac{0.178885}{2.236068} \approx 0.08$

The estimate of the firm value's constant volatility is 8%.

Explanation:

In the Merton model, the parameters $d_1$ and $d_2$ are related by the formula: $d_2 = d_1 - \sigma_V \sqrt{T}$

Where:

$d_1 = 3.217790$
$d_2 = 3.038905$
$T = 5 \text{ years}$
$\sigma_V$ is the firm value volatility.

Rearranging the formula to solve for $\sigma_V$ : $\sigma_V = \frac{d_1 - d_2}{\sqrt{T}}$ $\sigma_V = \frac{3.217790 - 3.038905}{\sqrt{5}}$ $\sigma_V = \frac{0.178885}{2.236068} \approx 0.08$

The estimate of the firm value's constant volatility is 8%.

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Question
A portfolio manager at a hedge fund is applying the Merton model to estimate the volatility of a non-dividend-paying firm whose equity shares are held in the fund’s portfolio. The manager conducts preliminary analysis on the firm and obtains the following results:

Value of equity: USD 45 million

Value of the firm’s only debt maturing in 5 years: USD 60 million

d₁: 3.217790

d₂: 3.038905

Assuming a constant volatility of firm value, what is the estimate of that volatility?

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Last updated: July 5, 2026 at 07:29

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