Variance Dynamics: Joint Evidence from Options and High-Frequency Returns

Abstract

With a portfolio of options on S&P 500 index, the Chicago Board of Options Exchange constructs a volatility index named VIX that approximates the 30-day return variance swap rate on the index. Using high-frequency return data, researchers have proposed various return quadratic variation estimators. This paper estimates the index return variance dynamics and variance risk premium jointly from the VIX index and various quadratic variation estimators constructed from tick data on S&P 500 index futures. Estimation shows that the index return variance jumps. The jump arrival rate is not constant over time, but proportional to the variance rate level. Furthermore, jumps in the index return variance are not rare events, but arrive frequently and generate sample paths that show infinite variation. Estimation also identifies a strongly negative variance risk premium, the absolute magnitude of which is proportional to the variance rate level. Finally, the estimation highlights the importance and necessity for removing microstructure noise in estimating quadratic variations.

Keywords: Return variance dynamics, variance risk premium, options, variance swap rates, high-frequency returns, market microstructure, realized variance, quadratic variation, time-changed Levy processes

JEL Classification: C13, C51, G12, G13