Abstract
We investigate the joint dynamics of spot and implied volatility from an
empirical perspective. We focus on the equity market with the SPX Index our
underlying of choice. Using only observable quantities, we extract the
instantaneous variance curves implied by the market and study their daily
variations jointly with spot returns. We analyze the characteristics of their
individual and joint densities, quantify the non-linear relationship between
spot and volatility, and discuss the modeling implications on the implied
leverage and the volatility clustering effects. We show that non-linearities
have little impact on the dynamics of at-the-money volatilities, but can have a
significant effect on the pricing and hedging of volatility derivatives.
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