Restoring Corrupted Cross-Recurrence Plots Using Matrix Completion: Application on the Time-Synchronization Between Market and Volatility Indexes

Abstract

The success of a trading strategy can be significantly enhanced by tracking accurately the implied volatility changes, which refers to the amount of uncertainty or risk about the degree of changes in a market index. This fosters the need for accurate estimation of the time-synchronization profile between a given market index and its associated volatility index. In this chapter, we advance existing solutions, which are based widely on the typical correlation, for identifying this temporal interdependence. To this end, cross-recurrence plot (CRP) analysis is exploited for extracting the underlying dynamics of a given market and volatility indexes pair, along with their time-synchronization profile. However, CRPs of degraded quality, for instance due to missing information, may yield a completely erroneous estimation of this profile. To overcome this drawback, a restoration stage based on the concept of matrix completion is applied on a corrupted CRP prior to the estimation of the time-synchronization relationship. A performance evaluation on the S&P 500 index and its associated VIX volatility index reveals the superior capability of our proposed approach in restoring accurately their CRP and subsequently estimating a temporal relation between the two indexes even when \(80\,\%\) of CRP values are missing.