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Option pricing with conditional GARCH models

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  • Escobar-Anel, Marcos
  • Rastegari, Javad
  • Stentoft, Lars

Abstract

This paper introduces a class of conditional GARCH models that offers significantly added flexibility to accommodate empirically relevant features of financial asset returns while admitting closed-form recursive solutions for the moment generating function, a variance dependent pricing kernel and, therefore, efficient option pricing in a realistic setting. This class of conditional GARCH models can be constructed with specifications of the GARCH dynamics and innovations, for which recursive moment generating function formulas have been derived, hence generalizing such families of models. As an example, we combine the popular Heston-Nandi model with Regime Switching to illustrate the flexibility of our methodology and demonstrate the importance in terms of option prices and Greeks of accommodating crisis periods and state dependency as well as priced variance risk.

Suggested Citation

  • Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2021. "Option pricing with conditional GARCH models," European Journal of Operational Research, Elsevier, vol. 289(1), pages 350-363.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:1:p:350-363
    DOI: 10.1016/j.ejor.2020.07.002
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    Cited by:

    1. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2023. "Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing," International Review of Financial Analysis, Elsevier, vol. 87(C).
    2. Ballestra, Luca Vincenzo & D’Innocenzo, Enzo & Guizzardi, Andrea, 2024. "A new bivariate approach for modeling the interaction between stock volatility and interest rate: An application to S&P500 returns and options," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1185-1194.
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    4. Nagaraj Naik & Biju R. Mohan, 2021. "Stock Price Volatility Estimation Using Regime Switching Technique-Empirical Study on the Indian Stock Market," Mathematics, MDPI, vol. 9(14), pages 1-18, July.

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    More about this item

    Keywords

    Pricing; GARCH models; Closed form solutions; Markov Chains; Non-normality;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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