Structural GARCH: The Volatility-Leverage Connection

Abstract

We propose a new model of volatility where financial leverage amplifies equity volatility by what we call the “leverage multiplier.” The exact specification is motivated by standard structural models of credit; however, our parameterization departs from the classic Merton (1974) model and can accommodate environments where the firm’s asset volatility is stochastic, asset returns can jump, and asset shocks are non-normal. In addition, our specification nests both a standard GARCH and the Merton model, which allows for a statistical test of how leverage interacts with equity volatility. Empirically, the Structural GARCH model outperforms a standard asymmetric GARCH model for approximately 74 percent of the financial firms we analyze. We then apply the Structural GARCH model to two empirical applications: the leverage effect and systemic risk measurement. As a part of our systemic risk analysis, we define a new measure called “precautionary capital” that uses our model to quantify the advantages of regulation aimed at reducing financial firm leverage.