Estimating Firm Leverage from Implied Put Volatility

Summary

The document raises a model implementation question about inferring a firm’s leverage from equity option prices. It describes using put implied volatilities within a structural credit risk framework, citing the Hull, Nelken, and White approach and a related CreditGrades implementation that also uses equity derivatives. The author attempts a specific CreditGrades case and observes unstable leverage estimates: small changes in option strike lead to large swings, and calculated values are sometimes negative.

No answer or proposed remedy is included, so the document provides no evidence about whether these outcomes are expected or indicate an implementation error. It establishes a useful calibration concern rather than teaching a complete estimation procedure. Readers would need the underlying model equations, option inputs, parameter constraints, and diagnostics to determine whether instability reflects sensitivity in the model or a mistake in the implementation.

Key ideas

• Structural credit models can use equity option implied volatility to infer market-implied firm leverage.
• The author reports high sensitivity of estimated leverage to small changes in put strike.
• The attempted implementation sometimes produces negative leverage estimates.
• The document does not establish whether the instability is a model property or a coding error.

Tags

# Using Put Volatilities to Estimate Firm Leverage/Credit Risk


# Using Put Volatilities to Estimate Firm Leverage/Credit Risk












This paper by Hull, Nelken and White uses implied volatilities in structural credit risk models to back out a market-implied leverage ratio. CreditGrades has a similar implementation using equity derivatives as well. My goal is to use these approaches to back out firm leverage.

I have tried to replicate the CreditGrades Approach using their Case C Approach. I notice, however, that the leverage ratio derived from the implied put volatilities is extremely volatile, and very small changes in the strike price can produce massive fluctuations in the leverage. The leverage ratio is also occasionally negative.

Does anybody have any experience in implementing this approach? Are these potentially normal/known issues with the model or is it likely that my implementation is flawed? I can upload my spreadsheet if need be.

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