Efficient Sampling for Realized Variance Estimation in Time-Changed Diffusion Models

Paper: arXiv 2212.11833

Authors: Timo Dimitriadis, Roxana Halbleib, Jeannine Polivka, Jasper Rennspies, Sina Streicher, Axel Friedrich Wolter

Abstract

This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most efficient under either hitting time sampling that samples whenever the price changes by a pre-determined threshold, or under the new concept of realized business time that samples according to a combination of observed trades and estimated tick variance. The analysis builds on the assumption that asset prices follow a diffusion that is time-changed with a jump process that separately models the transaction times. This provides a flexible model that allows for leverage specifications and Hawkes-type jump processes and separately captures the empirically varying trading intensity and tick variance processes, which are particularly relevant for disentangling the driving forces of the sampling schemes. Extensive simulations confirm our theoretical results and show that for low levels of noise, hitting time sampling remains superior while for increasing noise levels, realized business time becomes the empirically most efficient sampling scheme. An application to stock data provides empirical evidence for the benefits of using these intrinsic sampling schemes to construct more efficient RV estimators as well as for an improved forecast performance.

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 rigorous theoretical framework using time-changed diffusions and Hawkes processes to optimize Realized Variance estimators. It backs up its complex finite-sample derivations with comprehensive Monte Carlo simulations and empirical applications to stock data, proving strong practical and theoretical value.

Research Flowchart

  flowchart TD
    A[Goal: Efficient RV Estimation via Intrinsic Time Sampling] --> B[Model: Time-Changed Diffusion with Hawkes Jump Process]
    B --> C[Data Inputs: High-Frequency Stock Data & Noise Levels]
    C --> D[Sampling Strategies]
    D --> E[Hitting Time Sampling: Threshold Price Changes]
    D --> F[Realized Business Time: Trades + Estimated Tick Variance]
    E & F --> G[Theoretical Proofs, Simulations & Forecasting]
    G --> H[Outcomes: Hitting Time best for low noise; RBT best for high noise & forecasting]