Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions: Disentangling the Multi-Dimensional Variations in S&P 500 Index Options

Abstract:     
The equity index and index volatility interact through several distinct channels. First, holding business risk fixed, an increase in the level of financial leverage raises the level of the equity volatility. Second, regardless of the level of financial leverage, a positive shock to business risk increases the cost of capital and reduces the valuation of future cash flows, generating an instantaneous negative correlation between asset returns and asset volatility. Finally, the market experiences both small continuous movements and large market disruptions. The large and negative market disruptions often generate self-exciting behaviors. The occurrence of one disruption induces more disruptions to follow, thus raising market volatility. We propose an equity index dynamics that capture all three channels of interactions through the separate modeling of the asset return dynamics and the financial leverage variation. We analyze how the different sources of variations impact the index options behaviors differently across a wide range of strikes, maturities, and calendar days.

Keywords: Option pricing, implied volatility, leverage effect, volatility feedback, self-exciting, market disruptions, jumps, constant elasticity of variance, time-changed Levy processes, Fast Fourier Transform, Gauss-Hermite quadrature, unscented Kalman filter

JEL Classifications: F34, G12, G13

Working Paper Series