Low-Rank Structured Prediction for Instantaneous Volatility

Abstract: This talk is based on two papers: Matrix-based Prediction Approach for Intraday Instantaneous Volatility Vector (Choi and Kim, forthcoming, JBES) and Low-Rank Structured Nonparametric Prediction of Instantaneous Volatility (Choi and Kim).

The first paper introduces a novel method for predicting intraday instantaneous volatility within the Itô semimartingale framework. Stylized features of volatility time series—such as interday autoregressive dynamics and the intraday U-shaped pattern—are well documented.

To accommodate these features, we propose an interday-by-intraday instantaneous volatility matrix process that can be decomposed into a low-rank conditional expected volatility component and a noise component.

For prediction, we introduce the Two-sIde Projected-PCA (TIP-PCA) procedure. The second paper develops a nonparametric prediction method for the future intraday instantaneous volatility process during trading hours, leveraging both previous days’ data and the current day’s observed intraday path.

Our approach adopts the same interday-by-intraday matrix representation, decomposed into a low-rank conditional expectation and a noise matrix. Based on this structure, we propose the Structural Intraday-volatility Prediction (SIP) procedure to predict the future conditional expected volatility vector.