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Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index

Author

Listed:
  • Shin-Yun Wang

    (National Dong Hwa University)

  • Ming-Che Chuang

    (Feng Chia University)

  • Shih-Kuei Lin

    (National Chengchi University)

  • So-De Shyu

    (Takming University of Science and Technology)

Abstract

This study incorporates the Markov switching model with return jumps to depict the behavior of stock returns. Based on the daily Standard & Poor’s 500 index (hereafter SPX) and the daily closing price of the call option, we use the particle filtering algorithm to fit the parameter of the model. The joint log-likelihood evaluates the model performance: the weighted average log-likelihood with the rate of return of the SPX and the relative implied volatility root-mean-squared error for the SPX call options. The empirical results identify that the pricing model with jump risks improves the pricing performance to the median-term call options. According to the sensitivity analysis, option prices increase with the probability of remaining in the recession state but decrease with the probability of remaining in the expansion state. Moreover, the call option prices are positively associated with the volatility in each market state and the factors of jump risk.

Suggested Citation

  • Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    • Handle: RePEc:kap:rqfnac:v:56:y:2021:i:1:d:10.1007_s11156-020-00885-x
    DOI: 10.1007/s11156-020-00885-x
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    More about this item

    Keywords

    Markov switching; Jump risks; Volatility smile; Particle filter algorithm;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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