Structural GARCH: The Volatility-Leverage Connection

by Robert F. Engle & Emil N. Siriwardane

Overview — The financial crisis revealed the damaging role of financial market leverage on the economy. Even so, it is far from clear that reducing this leverage will stabilize the real economy, let alone stabilize the financial sector. A critical question remaining is how much reduction in equity volatility can be expected from reductions in leverage. To answer this question, the authors provide an econometric approach to disentangle the effects of leverage on equity volatility. Their framework has applications in measuring credit spreads, improving risk management, and assessing the impact of capital injections on financial sector risk.

Author 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.