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

Yipeng Yang and Allanus Tsoi
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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

IJFS, 2016, vol. 4, issue 1, 1-24

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.

Keywords: level set analysis; nonparametric regression; ARCH/GARCH model; prospect theory; behavioral finance; agent-based modeling (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2016
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