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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.

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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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