On the Number of State Variables in Options Pricing

作     者：Li, Gang Zhang, Chu 

作者机构：Hong Kong Baptist Univ Kowloon Tong Hong Kong Peoples R China Hong Kong Univ Sci & Technol Kowloon Hong Kong Peoples R China 

出 版 物：《MANAGEMENT SCIENCE》 (运筹学)

年 卷 期：2010年第56卷第11期

页      面：2058-2075页

核心收录：

学科分类：12[管理学] 120202[管理学-企业管理（含：财务管理、市场营销、人力资源管理）] 0202[经济学-应用经济学] 02[经济学] 1202[管理学-工商管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 

基　　金：RGC [HKUST646007] 

主　　题：options pricing state variables nonparametric method nonlinear principal component analysis 

摘      要：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.