Asset Volatility, Equity and Debt Values in the Merton Model

Summary

This note explains how asset volatility affects equity and debt in the Merton structural model. Equity is treated as a call option on firm assets, so greater volatility raises its value. Debt can be viewed as risk-free debt minus a put option, or equivalently as a position short an option; greater volatility therefore lowers debt value.

The answer also identifies a shareholder incentive: because equity holders benefit from increased volatility in this model, they may prefer riskier projects. This is a model-based implication rather than a general rule for every financing arrangement. The brief exchange gives no derivation, empirical evidence, or discussion of model assumptions, so it serves as a conceptual explanation rather than a practical valuation guide.

Key ideas

• In the Merton model, equity behaves like a call option on the firm's assets.
• Higher asset volatility increases the value of equity.
• Debt value falls as asset volatility rises because debt holders are exposed to the short-option side of the structure.
• The model implies that equity holders may favor projects that increase asset volatility.

Tags

# Relationship between asset volatility and debt and equity value


# Relationship between asset volatility and debt and equity value












So how I understand it, higher asset volatility implies a higher call option price. The Merton Model holds that the value of equity is a call option. This therefore implies that the equity value must increase as well. Assuming this is correct (which it very well might not be), how is the value of debt affected? Does it stay the same? By Merton's model, debt is a 'short put', so theoretically, it should also increase?

Also, if my interpretation of the relationship between asset volatility and equity value is correct, does this mean that equity holders will partake in riskier projects to maximise their value? Or is there something i'm missing.

Sorry if I sound like I have no idea what I'm talking about - as that might actually be the case...

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/42626

You're right about the equity value increasing with higher volatility. You're wrong about the debt value. That decreases with higher volatility, because it is short an option. And yes, equity holders have an incentive to increase volatility, at least in that model.

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