On the Number of State Variables in Options Pricing

Authors:
Gang Li;Chu Zhang
Affiliations:
Hong Kong Baptist University, Kowloon Tong, Hong Kong/ and Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Hong Kong Baptist University, Kowloon Tong, Hong Kong/ and Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
Management Science
Year:
2010

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Abstract

In this paper, we investigate the methodological issue of determining the number of state variables required for options pricing. After showing the inadequacy of the principal component analysis approach, which is commonly used in the literature, we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables. The methodology is applied to the prices of S&P 500 index options from the period 1996--2005. We find that, in addition to the index value itself, two state variables, approximated by the first two nonlinear principal components, are adequate for pricing the index options and fitting the data in both time series and cross sections.