Time-Varying Deterministic Volatility Model for Options on Wheat Futures †
Abstract
:1. Introduction
2. Literature Review
Integrated Volatility Models
3. Data Description
3.1. Wheat Futures
3.2. Wheat Option Contracts and Implied Volatility
3.3. Storage Data
4. Methodology for Volatility Analysis
4.1. Time to Maturity and Seasonality
4.1.1. Volatility Level Calibration
4.1.2. Parameter Calibration
4.2. Impact of Storage
“Large spikes are obviously quite rare in the available data. Even adding lesser spikes does not give us a sample useful for statistical analysis. Hence we must resort to a less formal analysis of the evidence.” [34], p. 50
4.3. Model Comparison
Forecast Comparison
5. Empirical Results
5.1. Seasonality and Time to Maturity
Parameter Interpretation
5.2. Storage Dynamics
5.3. Out-of-Sample Model Comparison
Parameter Stability
6. Black’s Option Pricing Model Extension
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Panel A: Stocks-to-Use Ratio < 25% | Panel B: Stocks-to-Use Ratio ≥ 25% | |||||||
---|---|---|---|---|---|---|---|---|
Chicago | 0.21 *** | −0.22 *** | −0.12 * | 0.05 | 0.10 | −0.23 *** | −0.31 *** | 0.17 * |
Kansas | 0.31 *** | −0.17 *** | 0.00 | −0.06 * | 0.12 *** | −0.17 *** | −0.13 *** | 0.07 *** |
Minneapolis | 0.36 *** | −0.18 *** | 0.05 | −0.13 *** | 0.13 *** | −0.24 *** | −0.22 *** | 0.13 *** |
Paris | 0.26 *** | −0.38 *** | 0.03 * | 0.07 *** | 0.15 *** | −0.28 *** | −0.37 *** | 0.24 *** |
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Panel A: Model–S | Panel B: Model–ST | |||||
---|---|---|---|---|---|---|
Exchange | ||||||
Chicago | 0.21 *** | −0.21 *** | 0.14 ** | −0.22 ** | −0.24 ** | 0.14 *** |
Kansas | 0.19 *** | −0.16 *** | 0.14 *** | −0.15 *** | −0.15 *** | 0.07 *** |
Minneapolis | 0.22 *** | −0.22 *** | 0.17 *** | −0.22 *** | −0.18 * | 0.11 *** |
Paris | 0.19 *** | −0.31 *** | 0.13 *** | −0.38 *** | −0.27 *** | 0.18 ** |
Panel A: Stocks-to-Use Ratio < 23% | Panel B: Stocks-to-Use Ratio ≥ 23% | |||||||
---|---|---|---|---|---|---|---|---|
Chicago | 0.25 *** | −0.13 *** | 0.03 | 0.02 | 0.12 *** | −0.25 *** | −0.31 *** | 0.16 *** |
Kansas | 0.20 *** | −0.05 | −0.10 | 0.08 | 0.14 *** | −0.18 *** | −0.16 *** | 0.08 *** |
Minneapolis | 0.17 *** | −0.00 | −0.22 *** | 0.18 *** | 0.19 *** | −0.25 *** | −0.19 *** | 0.10 ** |
Paris | 0.10 ** | −0.37 *** | 0.10 ** | −0.03 | 0.14 *** | −0.39 *** | −0.40 *** | 0.25 *** |
Panel A: Wheat—Chicago | |||
Implied Volatility | |||
30-day volatility | 13.95 *** | 10.55 *** | 17.21 *** |
−11.57 *** | 10.97 *** | ||
12.94 *** | |||
Panel B: Wheat—Minneapolis | |||
implied volatility | |||
30-day volatility | 13.78 *** | 5.96 *** | 10.85 *** |
−15.51 *** | 7.38 *** | ||
9.56 *** | |||
Panel C: Wheat—Kansas | |||
implied volatility | |||
30-day volatility | 11.29 *** | 7.54 *** | 9.17 *** |
−11.49 *** | 4.72 *** | ||
7.42 *** | |||
Panel D: Wheat—Paris | |||
implied volatility | |||
30-day volatility | 10.38 *** | 8.67 *** | 10.22 *** |
−8.7 *** | 6.1 *** | ||
7.64 *** |
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Haase, M.; Henn, J. Time-Varying Deterministic Volatility Model for Options on Wheat Futures. Commodities 2024, 3, 334-354. https://doi.org/10.3390/commodities3030019
Haase M, Henn J. Time-Varying Deterministic Volatility Model for Options on Wheat Futures. Commodities. 2024; 3(3):334-354. https://doi.org/10.3390/commodities3030019
Chicago/Turabian StyleHaase, Marco, and Jacqueline Henn. 2024. "Time-Varying Deterministic Volatility Model for Options on Wheat Futures" Commodities 3, no. 3: 334-354. https://doi.org/10.3390/commodities3030019
APA StyleHaase, M., & Henn, J. (2024). Time-Varying Deterministic Volatility Model for Options on Wheat Futures. Commodities, 3(3), 334-354. https://doi.org/10.3390/commodities3030019