On the number of state variables in options pricing

Gang LI*, Chu Zhang

*Corresponding author for this work

    Research output: Contribution to journalJournal articlepeer-review

    25 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)2058-2075
    Number of pages18
    JournalManagement Science
    Issue number11
    Publication statusPublished - Nov 2010

    Scopus Subject Areas

    • Strategy and Management
    • Management Science and Operations Research

    User-Defined Keywords

    • Nonlinear principal component analysis
    • Nonparametric method
    • Options pricing
    • State variables


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