Does the Firm-Specific Asset Volatility Process Implied by the Equity Market Revert to a Constant Value?

Abstract

In this paper, two structural models where firms have stationary capital structures and endogenous default barriers are extended to allow the principal value of a firm's debt to grow at a constant rate. This allows firms to have a dynamic capital structure. These two models are then used in conjunction with observable equity data to calculate the implied asset volatilities of a sample of fifty firms. Unit root tests are applied to the implied asset volatility and equity volatility processes to determine whether the processes are mean-reverting. Evidence that asset volatility is mean-reverting is found for forty-six of the fifty firms in the sample, regardless of which structural model is used to calculate the asset volatility, while the number of firms whose equity volatility is mean-reverting is in general lower for the poorer credit classes, consistent with the leverage effect. The mean-reversion of asset volatility has implications for the modelling of both equity and debt, and for the pricing of equity options, corporate bonds and credit derivatives.