Option-Pricing Based Distress Prediction Formula
The ingenious formula, which predicts default better than Altman’s Z-score, was developed by Robert C. Merton.
I’ll try to explain the logic behind the formula in simple terms.
It fundamentally relies on the Black-Scholes formula for pricing European call options. Merton refined this formula to account for dividend payouts, as dividends affect the stock price and consequently the option price.
He then viewed the company’s equity as the value of a European call option on the company’s total assets, with the exercise price being the amount of the debt. This led to formula 9.6, which essentially is the formula for the price of a call option on a dividend-paying stock but calculates the value of equity based on the value of the debt and the assets.
Essentially, Merton interpreted -d1 as the difference between the asset value and the debt amount, expressed in terms of standard deviations. The greater the value of the total assets compared to the debt, the lower the probability of default.
To derive this probability, he used the cumulative normal distribution function N[-d1].
Using this formula, it is possible to estimate the probability of a company’s default one, two, or three years in advance, depending on the term of the debt.
What’s significant is that academics affirm that it accurately reflects reality.
Option-Pricing Based Distress Prediction Formula – Excel
Corporate Valuation Theory, Evidence and Practice
Mark E. Zmijewski; Robert W. Holthausen
Second Edition