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On the Number of State Variables in Options Pricing

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  • Gang Li

    ()
    (Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Chu Zhang

    ()
    (Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

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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.

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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1222
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 11 (November)
    Pages: 2058-2075

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    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:11:p:2058-2075

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    Keywords: options pricing; state variables; nonparametric method; nonlinear principal component analysis;

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    Cited by:
    1. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
    2. Madan, Dilip B. & Schoutens, Wim, 2013. "Systemic risk tradeoffs and option prices," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 222-230.
    3. Adam Aleksander Majewski & Giacomo Bormetti & Fulvio Corsi, 2014. "Smile from the Past: A general option pricing framework with multiple volatility and leverage components," Papers 1404.3555, arXiv.org.
    4. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    5. repec:wyi:wpaper:002044 is not listed on IDEAS

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