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A Level Set Analysis and A Nonparametric Regression on S&P 500 Daily Return

Author

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  • Yipeng Yang

    () (Department of Mathematics and Statistics, University of Houston-Clear Lake, 2700 Bay Area Blvd., Houston, TX 77058, USA)

  • Allanus Tsoi

    () (Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA)

Abstract

In this paper, a level set analysis is proposed which aims to analyze the S&P 500 return with a certain magnitude. It is found that the process of large jumps/drops of return tend to have negative serial correlation, and volatility clustering phenomenon can be easily seen. Then, a nonparametric analysis is performed and new patterns are discovered. An ARCH model is constructed based on the patterns we discovered and it is capable of manifesting the volatility skew in option pricing. A comparison of our model with the GARCH(1,1) model is carried out. The explanation of the validity on our model through prospect theory is provided, and, as a novelty, we linked the volatility skew phenomenon to the prospect theory in behavioral finance.

Suggested Citation

  • Yipeng Yang & Allanus Tsoi, 2016. "A Level Set Analysis and A Nonparametric Regression on S&P 500 Daily Return," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 4(1), pages 1-24, February.
  • Handle: RePEc:gam:jijfss:v:4:y:2016:i:1:p:3-:d:63997
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    level set analysis; nonparametric regression; ARCH/GARCH model; prospect theory; behavioral finance; agent-based modeling;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • F42 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Policy Coordination and Transmission

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