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The Journal of Derivatives
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An Improved Estimation Method for a Family of GARCH Models

Pascal Létourneau
The Journal of Derivatives Fall 2019, 27 (1) 67-91; DOI: https://doi.org/10.3905/jod.2019.1.081
Pascal Létourneau
is an assistant professor in the Department of Finance and Business Law at the University of Wisconsin-Whitewater, in Whitewater, WI
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Abstract

This article proposes an improved estimation and calibration method to a family of GARCH models. The suggested method fixes one parameter such that the unconditional kurtosis of the model matches the sample kurtosis. An empirical analysis using Engle and Ng’s (1993) NGARCH(1,1) model shows that the method dominates previous estimation methods in multiple ways. The optimization problem is simplified and made less sensitive to initial values. The optimization time, both when estimating based on historical returns and calibrating to option prices, is reduced by roughly 50%. The in-sample fit is barely affected, while the option pricing, both in sample and out of sample, is improved.

TOPICS: Statistical methods, quantitative methods, options, derivatives

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The Journal of Derivatives: 27 (1)
The Journal of Derivatives
Vol. 27, Issue 1
Fall 2019
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An Improved Estimation Method for a Family of GARCH Models
Pascal Létourneau
The Journal of Derivatives Aug 2019, 27 (1) 67-91; DOI: 10.3905/jod.2019.1.081

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An Improved Estimation Method for a Family of GARCH Models
Pascal Létourneau
The Journal of Derivatives Aug 2019, 27 (1) 67-91; DOI: 10.3905/jod.2019.1.081
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  • Article
    • Abstract
    • GENERAL GARCH(1,1) MODEL
    • ESTIMATION AND CALIBRATION
    • STANDARD QUASI-MAXIMUM-LIKELIHOOD ESTIMATION
    • KURTOSIS-TARGETING ESTIMATION
    • VTE AND COMBINED VKTE
    • CALIBRATION OF THE RISK-NEUTRAL DYNAMICS TO OPTION PRICES
    • RESULTS AND DISCUSSIONS
    • DATA
    • ESTIMATION RESULTS
    • CALIBRATION RESULTS
    • OPTION PRICING RESULTS
    • OUT-OF-SAMPLE OPTION PRICING
    • ROBUSTNESS TESTS
    • CONCLUSION AND FURTHER RESEARCH
    • ADDITIONAL READING
    • ACKNOWLEDGMENTS
    • APPENDIX A
    • APPENDIX B
    • ENDNOTES
    • REFERENCES
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