High-Frequency Volatility Estimation with Fast Multiple Change Points Detection

Paper: arXiv 2303.10550

Authors: Greeshma Balabhadra, El Mehdi Ainasse, Pawel Polak

Abstract

We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are $\ell_1$-regularized versions of existing volatility estimators. We focus on power variation estimators as they represent a fundamental class of volatility estimators. We establish consistency of these estimators for the true unobserved volatility and the change points locations, showing that minimax rates can be achieved for particular volatility estimators. The new estimators utilize the computationally efficient least angle regression algorithm for estimation purposes, followed by a reduced dynamic programming step to refine the final number of change points. In terms of numerical performance, these estimators are not only computationally fast but also accurately identify breakpoints near the end of the sample, both features highly desirable in today’s electronic trading environment. In terms of out-of-sample volatility prediction, our new estimators provide more realistic and smoother volatility forecasts, outperforming a broad range of classical and recent volatility estimators across various frequencies and forecasting horizons.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically rigorous framework combining L1-regularization, least angle regression (LARS), and dynamic programming to address change points in high-frequency spot volatility. It strongly connects theoretical minimax rates with superior out-of-sample empirical forecasting performance, making it highly valuable for real-time electronic trading applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Fast, Sparse High-Frequency<br>Volatility Estimation with Change Points] --> B[Data Inputs: High-Frequency Equity Prices<br>& Power Variation Estimators]
    B --> C[Step 1: Construct L1-Regularized Estimators<br>via Least Angle Regression - LARS]
    C --> D[Step 2: Refine Breakpoint Locations<br>using Reduced Dynamic Programming]
    D --> E[Outcomes: Consistent Spot Volatility &<br>Minimax Rate Change Point Detection]
    D --> F[Outcomes: Fast End-of-Sample Breakpoint<br>Detection & Smoother Volatility Forecasts]