Log Heston Model for Monthly Average VIX
Statistical Finance
2024-10-31 v1 Applications
Abstract
We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing them by VIX) makes them much closer to independent identically distributed Gaussian. The resulting model is mean-reverting, and the innovations are non-Gaussian. The combined stochastic volatility model fits well, and captures Pareto-like tails of real-world stock market returns. This works for small and large stock indices, for both price and total returns.
Keywords
Cite
@article{arxiv.2410.22471,
title = {Log Heston Model for Monthly Average VIX},
author = {Jihyun Park and Andrey Sarantsev},
journal= {arXiv preprint arXiv:2410.22471},
year = {2024}
}
Comments
12 pages, 5 figures, 17 graphs. Keywords: autoregression, volatility, Hill estimator, variance-gamma distribution, stationary Markov chain