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The Journal of Derivatives

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Article

Long and Short Memory in the Risk-Neutral Pricing Process

Young Shin Kim, Danling Jiang and Stoyan Stoyanov
The Journal of Derivatives Summer 2019, 26 (4) 71-88; DOI: https://doi.org/10.3905/jod.2019.1.077
Young Shin Kim
is an assistant professor of finance in the College of Business at Stony Brook University in Stony Brook, NY
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Danling Jiang
is a professor of finance in the College of Business at Stony Brook University in Stony Brook, NY, and the School of Economics and Management at Southwest Jiaotong University in Chengdu, China
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Stoyan Stoyanov
is a research professor of finance in the College of Business at Stony Brook University in Stony Brook, NY
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Abstract

This article proposes a semi-martingale approximation to a fractional Lévy process that is capable of capturing long and short memory in the stochastic process together with fat tails. The authors use the semi-martingale process in option pricing and empirically compare its performance to other option pricing models, including a stochastic volatility Lévy process. They contribute to the empirical literature by being the first to report the implied Hurst index computed from observed option prices using the Lévy process model. Calibrating the implied Hurst index of S&P 500 option prices in a period that covers the 2008 financial crisis, they find that the risk-neutral measure is characterized by a short memory in turbulent markets and a long memory in calm markets.

TOPICS: Options, statistical methods, performance measurement

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The Journal of Derivatives: 26 (4)
The Journal of Derivatives
Vol. 26, Issue 4
Summer 2019
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Long and Short Memory in the Risk-Neutral Pricing Process
Young Shin Kim, Danling Jiang, Stoyan Stoyanov
The Journal of Derivatives May 2019, 26 (4) 71-88; DOI: 10.3905/jod.2019.1.077

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Long and Short Memory in the Risk-Neutral Pricing Process
Young Shin Kim, Danling Jiang, Stoyan Stoyanov
The Journal of Derivatives May 2019, 26 (4) 71-88; DOI: 10.3905/jod.2019.1.077
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  • Article
    • Abstract
    • FRACTIONAL RAPIDLY DECREASING TEMPERED STABLE MODEL
    • OPTION PRICING WITH THE fR-RDTS PROCESS
    • EMPIRICAL ILLUSTRATIONS
    • CONCLUSION
    • ACKNOWLEDGMENTS
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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