Variance Dynamics - An empirical journey

TL;DR

This paper empirically examines the joint behavior of spot prices and implied volatility in the equity market, revealing non-linear relationships and their implications for volatility modeling and derivatives pricing.

Contribution

It introduces a method to extract and analyze instantaneous variance curves from observable data, highlighting the impact of non-linearities on volatility dynamics and derivatives.

Findings

Non-linearities minimally affect at-the-money volatility dynamics.

Significant impact of non-linearities on volatility derivatives pricing.

Empirical analysis based on SPX index data.

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.