On the number of state variables in options pricing

Gang LI*, Chu Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 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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