Theory and Applications of Financial Chaos Index

TL;DR

This paper introduces a novel tensor-based stock market index that measures market chaos and volatility without traditional weighting assumptions, revealing a causal influence of implied volatility on realized volatility.

Contribution

It develops a new chaos index using tensor embeddings, providing a robust measure of market volatility and insights into the causal relationship between implied and realized volatility.

Findings

The index effectively captures market chaos and volatility.

A bidirectional causal relationship exists between realized and implied volatility.

Implied volatility has a stronger causal effect on realized volatility.

Abstract

We develop a new stock market index that captures the chaos existing in the market by measuring the mutual changes of asset prices. This new index relies on a tensor-based embedding of the stock market information, which in turn frees it from the restrictive value- or capitalization-weighting assumptions that commonly underlie other various popular indexes. We show that our index is a robust estimator of the market volatility which enables us to characterize the market by performing the task of segmentation with a high degree of reliability. In addition, we analyze the dynamics and kinematics of the realized market volatility as compared to the implied volatility by introducing a time-dependent dynamical system model. Our computational results which pertain to the time period from January 1990 to December 2019 imply that there exist a bidirectional causal relation between the processes underlying the realized and implied volatility of the stock market within the given time period, where it is shown that the later has a stronger causal effect on the former as compared to the opposite. This result connotes that the implied volatility of the market plays a key role in characterization of the market's realized volatility.