A multivariate model for financial indices and an algorithm for detection of jumps in the volatility

TL;DR

This paper presents a multivariate stochastic volatility model with an algorithm to detect volatility jumps, applied to major stock indices, and demonstrates strong agreement between theoretical and empirical cross-asset correlation decay.

Contribution

It introduces a new algorithm for volatility jump detection and extends the model to a bivariate case with explicit correlation decay expressions.

Findings

Effective detection of volatility peaks in financial time series

Excellent match between theoretical and empirical correlation decay

Application to major stock indices over nearly three decades

Abstract

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of Dow Jones Industrial Average and Financial Times Stock Exchange 100 in the period 1984-2013. Based on empirical results, we propose a bivariate version of the model, for which we find an explicit expression for the decay over time of cross-asset correlations between absolute returns. We compare our theoretical predictions with empirical estimates on the same financial time series, finding an excellent agreement.