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On options-driven realized volatility forecasting: Information gains via rough volatility model

Zheqi Fan, Meng, Wang, Yifan Ye

Abstract

We examine whether model-based spot volatility estimators extracted from traded options data enhance the predictive power of the Heterogeneous Autoregressive (HAR) model for realized volatility. Specifically, we infer spot volatility under the rough stochastic volatility model via an iterative two-step approach following Andersen et al. (2015a) and adopt a deep learning surrogate to accelerate model estimation from large-scale options panels. Benchmarked against traditional stochastic volatility models (Heston, Bates, SVCJ) and the VIX index, our results demonstrate that the augmented HAR-RV-RHeston model improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month.

On options-driven realized volatility forecasting: Information gains via rough volatility model

Abstract

We examine whether model-based spot volatility estimators extracted from traded options data enhance the predictive power of the Heterogeneous Autoregressive (HAR) model for realized volatility. Specifically, we infer spot volatility under the rough stochastic volatility model via an iterative two-step approach following Andersen et al. (2015a) and adopt a deep learning surrogate to accelerate model estimation from large-scale options panels. Benchmarked against traditional stochastic volatility models (Heston, Bates, SVCJ) and the VIX index, our results demonstrate that the augmented HAR-RV-RHeston model improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month.

Paper Structure

This paper contains 20 sections, 2 theorems, 26 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Data and Realized Volatility
  3. Realized volatility
  4. Extracting volatility estimators under stochastic volatility models
  5. Rough Heston stochastic volatility model
  6. Deep surrogate for vanilla option pricing
  7. Parametric inference
  8. Implementation details of iterative two-step procedure
  9. Empirical results
  10. HAR and HARX Models
  11. Forecast evaluation
  12. In-sample results
  13. Out-of-sample
  14. Multiple horizons of forecasting power
  15. Future research
  16. ...and 5 more sections

Key Result

Lemma C.1

where and $h$ is a solution of the following fractional Riccati equation: with $D^\alpha$ and $I^{1-\alpha}$, for $\alpha \in(0,1]$, the fractional derivative and integral operators defined as Remark that when $\alpha=1$, this result indeed coincides with the classical Heston's result. However, note that for $\alpha<1$, the solutions of such Riccati equations are no longer explicit. Nevertheles

Figures (6)

  • Figure 1: Realized volatility from high frequency returns
  • Figure 2: Accuracy for pre-trained deep surrogate
  • Figure 3: Flowchart of the parametric inference procedure
  • Figure 4: Spot volatility estimators from SV model
  • Figure 5: Boxplots of forecast errors for models
  • ...and 1 more figures

Theorems & Definitions (5)

  • Remark 3.1
  • Lemma C.1: Characteristic function under the rough Heston model
  • proof
  • Lemma C.2: Characteristic function under the lifted Heston model
  • proof