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Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse

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  • Young Shin Kim

Abstract

This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets.

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  • Young Shin Kim, 2016. "Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(4), pages 309-322, July.
    • Handle: RePEc:taf:apmtfi:v:23:y:2016:i:4:p:309-322
    DOI: 10.1080/1350486X.2016.1268926
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    Cited by:

    1. Aurelio F. Bariviera & Angelo Plastino & George Judge, 2018. "Spurious Seasonality Detection: A Non-Parametric Test Proposal," Econometrics, MDPI, vol. 6(1), pages 1-15, January.
    2. Ma, Chao & Ma, Qinghua & Yao, Haixiang & Hou, Tiancheng, 2018. "An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 87-117.

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