Equity Inputs for the Merton Corporate Debt Model

Summary

The note clarifies which equity measures to use when applying the standard Merton model to a publicly traded company. It recommends market capitalization as the equity value and the stock’s implied volatility as its volatility input, with at-the-money implied volatility offered as a sensible choice. These are market-based measures, rather than balance-sheet equity or a volatility index.

The response contrasts publicly traded firms with private companies, for which the necessary market figures may not be available. It does not explain how to estimate the model’s other inputs, compare implied volatility with historical volatility, or test alternative volatility conventions. The advice is brief and should be treated as a suggested input choice rather than a detailed validation of the model.

Key ideas

• Use market capitalization for the equity value of a publicly traded company in the standard Merton model.
• Use the stock’s implied volatility as the equity volatility input.
• At-the-money implied volatility is suggested as a reasonable convention.
• The response says the required market inputs may be unavailable for private companies.

Tags

# Finding Equity Volatility for the Standard Merton Model of Corporate Debt


# Finding Equity Volatility for the Standard Merton Model of Corporate Debt












I am working on a project studying historical accuracy of the standard Merton Model, but am struggling to follow the required inputs. I seem to read conflicting definitions of the information I need.

For example, equity. Does this refer to stock price, market cap, assets less liabilities on the balance sheet? What about equity volatility? Is this the standard deviation of returns? Some VIX interpretation? Which 'version' of equity is necessary here?

From looking around online, I have seen papers with daily Merton calculations, but that doesn't seem consistent with requiring information from a quarterly balance sheet.

Any help would be greatly appreciated.

## Answer by Bob Jansen (score 1)

https://quant.stackexchange.com/a/40899

If the company is publicly traded you can use the current market capitalization and the implied volatility of that stock (a choice must be made here, it seems sensible to use the ATM implied volatility).

For non-publicly traded companies it doesn't seem possible to use the Merton model as these figures can't be obtained.

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