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Learning for infinitely divisible GARCH models in option pricing

Author

Listed:
  • Zhu Fumin

    (College of Economics, Center for Finance & Accounting Research, Shenzhen University, Shenzhen, Guangdong, China)

  • Bianchi Michele Leonardo

    (Regulation and Macroprudential Analysis Directorate, Bank of Italy, Rome, Italy)

  • Kim Young Shin

    (College of Business, Stony Brook University, Stony Brook, NY, USA)

  • Fabozzi Frank J.

    (EDHEC Business School, Nice, France)

  • Wu Hengyu

    (Management School, Jinan University, Guangzhou, Guangdong, China)

Abstract

This paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

Suggested Citation

  • Zhu Fumin & Bianchi Michele Leonardo & Kim Young Shin & Fabozzi Frank J. & Wu Hengyu, 2020. "Learning for infinitely divisible GARCH models in option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(3), pages 35-62, June.
    • Handle: RePEc:bpj:sndecm:v:25:y:2020:i:3:p:35-62:n:4
    DOI: 10.1515/snde-2019-0088
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    More about this item

    Keywords

    Lévy–GARCH models; Markov chain Monte Carlo; option pricing; particle filtering; sequential Bayesian learning; G11; G12; G13; G17;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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