Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions

Equity index volatility variation and its interaction with the index return can come from three distinct channels. First, index volatility increases with the market's aggregate financial leverage. Second, positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows, generating a negative correlation between the index return and its volatility, regardless of financial leverage. Finally, large negative market disruptions show self-exciting behaviors. This article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies.