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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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    1. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    3. Jeff Fleming & Barbara Ostdiek & Robert E. Whaley, 1995. "Predicting stock market volatility: A new measure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(3), pages 265-302, May.
    4. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    5. Schwert, G. William, 1989. "Business cycles, financial crises, and stock volatility," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 31(1), pages 83-125, January.
    6. Turner, Christopher M. & Startz, Richard & Nelson, Charles R., 1989. "A Markov model of heteroskedasticity, risk, and learning in the stock market," Journal of Financial Economics, Elsevier, vol. 25(1), pages 3-22, November.
    7. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    9. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    10. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    11. Shiu-Sheng Chen, 2007. "Does Monetary Policy Have Asymmetric Effects on Stock Returns?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 667-688, March.
    12. Maheu, John M & McCurdy, Thomas H, 2000. "Identifying Bull and Bear Markets in Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 100-112, January.
    13. Chun-Chou Wu, 2006. "The GARCH Option Pricing Model: A Modification of Lattice Approach," Review of Quantitative Finance and Accounting, Springer, vol. 26(1), pages 55-66, February.
    14. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    15. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    16. Kim, Chang-Jin & Morley, James C & Nelson, Charles R, 2004. "Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 339-360, June.
    17. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    18. Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
    19. Chien-Hsiu Lin & Shih-Kuei Lin & An-Chi Wu, 2015. "Foreign exchange option pricing in the currency cycle with jump risks," Review of Quantitative Finance and Accounting, Springer, vol. 44(4), pages 755-789, May.
    20. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    21. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    22. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2005. "The Structural Break in the Equity Premium," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 181-191, April.
    23. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    24. 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.
    25. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    26. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    27. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    28. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    29. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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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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