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Characteristic Function-Based Factor Modeling of Affine Jump-Diffusions using Options

Author

Listed:
  • H. Peter Boswijk

    (University of Amsterdam)

  • Roger J. A. Laeven

    (University of Amsterdam)

  • Niels Marijnen

    (University of Amsterdam)

  • Evgenii Vladimirov

    (Erasmus University Rotterdam)

Abstract

We develop a framework to analyze option markets using factor modeling techniques, offering a novel method to study how many and which risk factors drive the price process of a single asset. We exploit information contained in option prices to construct observations on the characteristic function of the returns on the underlying asset, without having to specify a parametric model. Our asymptotic setting is one in which the number of observed options, with varying strikes, tends to infinity. We establish consistency and asymptotic normality of the option-based log-characteristic function estimator, and provide a feasible central limit theorem that can be used for testing. Based on this, we prove that principal component analysis is able to extract the factors of affine jump-diffusions. We show in Monte Carlo simulations that our has good finite-sample properties. An empirical application indicates that the main factor driving S&P 500 returns is a stochastic variance process, along with a factor related to left-tail jump risk, and that at least two factors are needed to explain higher-order moments with reasonable accuracy.

Suggested Citation

  • H. Peter Boswijk & Roger J. A. Laeven & Niels Marijnen & Evgenii Vladimirov, 2026. "Characteristic Function-Based Factor Modeling of Affine Jump-Diffusions using Options," Tinbergen Institute Discussion Papers 26-026/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20260026
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    References listed on IDEAS

    as
    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Kong, Xin-Bing & Liu, Zhi & Zhou, Wang, 2019. "A rank test for the number of factors with high-frequency data," Journal of Econometrics, Elsevier, vol. 211(2), pages 439-460.
    3. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    4. Büchner, Matthias & Kelly, Bryan, 2022. "A factor model for option returns," Journal of Financial Economics, Elsevier, vol. 143(3), pages 1140-1161.
    5. Christopher S. Jones, 2006. "A Nonlinear Factor Analysis of S&P 500 Index Option Returns," Journal of Finance, American Finance Association, vol. 61(5), pages 2325-2363, October.
    6. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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