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Estimating Private Firm Asset Volatility for Merton and KMV Models

Article Quant Q&A · Author: manu
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Summary

The discussion addresses how to estimate volatility for a private company when applying Merton or KMV credit risk models. The questioner has several years of accounting data but no public share prices, and wants to estimate each portfolio company's probability of default. The accepted response says accounting data alone will not supply the market-based volatility input sought by these models.

It proposes using volatility from public companies as a proxy, selecting firms in the same industry with similar growth stage and regulatory or legal conditions. The response cautions that even a carefully matched proxy will be a poor approximation. It also notes that Merton and KMV rely on substantial assumptions, so the resulting probability of default should be interpreted with care. The brief exchange offers no calculation procedure, validation evidence, or alternative calibration method; it is best read as a warning about the limits of applying structural credit models to private firms with sparse observable data.

Key ideas

  • The exchange concerns the volatility input needed to apply Merton or KMV models to private firms.
  • Accounting records alone are not presented as a sufficient estimate of the required volatility.
  • Public firms with similar industry, growth stage, and regulatory setting can serve as proxies.
  • Proxy volatility is described as a poor approximation, and model assumptions add further uncertainty.
  • The answer provides no empirical validation or detailed calibration recipe.

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StatisticsRisk management
Full text
# How to compute the volatility for the Merton's Model for Private firm?


# How to compute the volatility for the Merton's Model for Private firm?












After one day of research i did not figured how to compute the input volatility for PRIVATE COMPANY in order to calculate the PD.

My goal is to compute the PD of each of my company in my portfolio, all companies are private companies. To do that i found 2 models that can fit my expectation:

The Merton's Model and KMV model.

Problem for both I cannot figured it out how to calculate the volatility.

For your information, I have accounting data at least for 3 years up to 10 years for some companies.

I could send you my excel sheet if you would like. It is very important for me as it is part of my master thesis.

Thank you in advance for your help.

## Answer by phdstudent (score 3, accepted)

https://quant.stackexchange.com/a/20722

Accounting data won't work for what you are looking for. The only way to do it is to look to public firms on same industry, similar growth stage, same regulatory/legal challenges and compute the volatility of those and use it as a proxy for your firm. It is the best you will be able to get, and it will be a bad approximation. The Merton and KMV models already rely on some non-trivial assumptions.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.