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The role of the variance premium in Jump-GARCH option pricing models

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  • Byun, Suk Joon
  • Jeon, Byoung Hyun
  • Min, Byungsun
  • Yoon, Sun-Joong

Abstract

We develop a discrete-time option pricing model incorporating a variance-dependent pricing kernel of Christoffersen et al. (2013) under an economic framework allowing for dynamic volatility and jump intensity. Based on the model, we examine the role of the variance premium and jump risk premium in explaining S&P 500 index option prices and returns. According to the results, the variance premium is equally important as the jump risk premium in explaining the empirical option data. Whereas the incorporation of the jump risk premium improves the model fit on option prices, the incorporation of the variance premium improves the fit on option returns. In particular, the variance premium can explain both 1-month holding period returns of 2-month maturity straddles, which are significantly negative, and call returns, which decrease according to moneyness. The model incorporating the jump risk premium only has a limitation in explaining the above two stylized returns. The outperformance of the model incorporating the variance premium on option returns stems from its ability to capture the wedge between physical and risk-neutral volatilities.

Suggested Citation

  • Byun, Suk Joon & Jeon, Byoung Hyun & Min, Byungsun & Yoon, Sun-Joong, 2015. "The role of the variance premium in Jump-GARCH option pricing models," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 38-56.
  • Handle: RePEc:eee:jbfina:v:59:y:2015:i:c:p:38-56
    DOI: 10.1016/j.jbankfin.2015.05.009
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    Keywords

    Variance premium; Variance-dependent pricing kernel; Jump risk premium; S&P 500 index options; Jump-GARCH option pricing models;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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