What Equity Prices Tell Us About Default Risk

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🎯 One weakness of credit ratings is that they are updated relatively infrequently, while credit risk itself can change significantly over short periods of time. As it turns out, equity prices can help predict default risk.

The core idea is that the value of a company’s equity can be viewed as a call option on the company’s assets. As a result, the probability of default can be interpreted as a function of:

• the value of the firm’s assets,
• the volatility of those assets,
• and the firm’s financial leverage.

This idea belongs to Robert C. Merton, who extended the Black–Scholes framework into a practical model for estimating default probabilities.
(See in detail: Distress Prediction and the Merton Model)

One challenge with applying the Merton model is that we need to know:

• the market value of the firm’s assets,
• and the volatility of those assets.

However, these variables are not directly observable in the market.

Fortunately, Ito’s lemma allows us to infer these hidden parameters using observable market data.

Ito’s Lemma leads to the following relationship between asset volatility and equity volatility:

Symbol	Meaning
$\sigma_E$	Equity volatility
$E_0$	Current market value of equity
$\sigma_E E_0$	Dollar volatility of equity
$N(d_1)$	Sensitivity of equity to asset value
$\sigma_V$	Asset volatility
$V_0$	Current market value of firm assets
$\sigma_V V_0$	Dollar volatility of firm assets

Integrating this relationship into the option pricing framework gives:

Symbol	Meaning
$E_0$	Current market value of equity
$V_0$	Current market value of firm assets
$D$	Debt repayment due at maturity
$r$	Risk-free interest rate
$T$	Time to debt maturity
$e^{-rT}$	Discount factor
$N(d_1)$	Risk-adjusted asset participation in equity value
$N(d_2)$N(d2​)	Risk-neutral survival-related component

Finally, the probability of default is calculated as:

where:

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Important Note

An important nuance is that this framework produces a risk-neutral probability of default, not a real-world default probability.

In reality, the true probability of default would usually be lower because the model uses:

• option-pricing formulas,
• and the risk-free rate as the discount rate.

Nevertheless, the model remains highly useful in practice because it provides strong relative ranking signals across firms and allows markets to continuously reprice credit risk.

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📊 Excel – Default Probability Calculator

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📚 Source:

Options, Futures, and Other Derivatives