Paper: arXiv 2308.01419

Abstract

We present a novel methodology for modeling and forecasting multivariate realized volatilities using customized graph neural networks to incorporate spillover effects across stocks. The proposed model offers the benefits of incorporating spillover effects from multi-hop neighbors, capturing nonlinear relationships, and flexible training with different loss functions. Our empirical findings provide compelling evidence that incorporating spillover effects from multi-hop neighbors alone does not yield a clear advantage in terms of predictive accuracy. However, modeling nonlinear spillover effects enhances the forecasting accuracy of realized volatilities, particularly for short-term horizons of up to one week. Moreover, our results consistently indicate that training with the Quasi-likelihood loss leads to substantial improvements in model performance compared to the commonly-used mean squared error. A comprehensive series of empirical evaluations in alternative settings confirm the robustness of our results.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper utilizes advanced graph neural network architectures with multi-layer setups and specialized quasi-likelihood loss functions, indicating significant mathematical complexity. It also demonstrates high empirical rigor through comprehensive out-of-sample backtesting across market conditions, alternative data splits, and robustness checks using realized volatility data.

Research Flowchart

  flowchart TD
  A["Research Goal: Forecast Multivariate Realized Volatility<br>with Spillover Effects"] --> B["Input: Multivariate Equity Volatility Data"]
  B --> C{"Methodology: Customized GNN<br>with Multi-hop & Nonlinear Spillovers"}
  C --> D["Training: Comparison of<br>Quasi-Likelihood vs MSE Loss"]
  D --> E["Empirical Evaluation<br>in Alternative Settings"]
  E --> F{"Key Findings/Outcomes"}
  F --> F1["Nonlinear Spillovers<br>Improve Accuracy (1D-1W Horizon)"]
  F --> F2["Quasi-Likelihood Loss<br>Significantly Outperforms MSE"]
  F --> F3["Multi-hop Spillovers Alone<br>No Clear Advantage"]
  F --> F4["Results Robust<br>Across Alternative Settings"]