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Int. J. Financial Stud. 2016, 4(1), 3; doi:10.3390/ijfs4010003

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

1
Department of Mathematics and Statistics, University of Houston-Clear Lake, 2700 Bay Area Blvd., Houston, TX 77058, USA
2
Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Nicholas Apergis
Received: 12 October 2015 / Revised: 29 December 2015 / Accepted: 28 January 2016 / Published: 18 February 2016

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. View Full-Text
Keywords: level set analysis; nonparametric regression; ARCH/GARCH model; prospect theory; behavioral finance; agent-based modeling level set analysis; nonparametric regression; ARCH/GARCH model; prospect theory; behavioral finance; agent-based modeling
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Yang, Y.; Tsoi, A. A Level Set Analysis and A Nonparametric Regression on S&P 500 Daily Return. Int. J. Financial Stud. 2016, 4, 3.

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