Structural Stochastic Volatility

Résumé

We use a local (in time) expansion of the characteristic function of the equity process in continuous time to derive short-maturity option prices. The prices, along with data on short maturity options, are employed to jointly identify equity characteristics (spot volatility, spot leverage and spot volatility of volatility) which have been the focus of separate strands of the literature. We show that the proposed identification method yields measurements which are statistically accurate and economically revealing. Interpreting equity as a call option on asset values, all equity characteristics should depend on fundamental state variables, such as the variance of the firm's assets and the extent of the firm's financial leverage. Among other findings, consistent with economic logic, we document a strong link between spot leverage (the generally negative correlation between equity returns and spot volatility) and financial leverage (the firm's debt-to-equity ratio), a relation invariably found to be elusive in the data. We conclude that the economic content of option-implied measurements can be put to work to study the structural drivers of equity (and debt) return dynamics from a novel vantage point.