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Option pricing with state‐dependent pricing kernel

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  • Chen Tong
  • Peter Reinhard Hansen
  • Zhuo Huang

Abstract

We introduce a new volatility model for option pricing that combines Markov switching with the realized generalized autoregressive conditional heteroskedasticity (GARCH) framework. This leads to a novel pricing kernel with a state‐dependent variance risk premium and a pricing formula for European options, which is derived with an analytical approximation method. We apply the Markov‐switching Realized GARCH model to Standard and Poor's 500 index options from 1990 to 2019 and find that investors' aversion to volatility‐specific risk is time‐varying. The proposed framework outperforms competing models and reduces (in‐sample and out‐of‐sample) option‐pricing errors by 15% or more.

Suggested Citation

  • Chen Tong & Peter Reinhard Hansen & Zhuo Huang, 2022. "Option pricing with state‐dependent pricing kernel," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1409-1433, August.
    • Handle: RePEc:wly:jfutmk:v:42:y:2022:i:8:p:1409-1433
    DOI: 10.1002/fut.22338
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    1. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
    2. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    3. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    4. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    5. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    6. 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.
    7. Bekaert, Geert & Hoerova, Marie & Lo Duca, Marco, 2013. "Risk, uncertainty and monetary policy," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 771-788.
    8. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2008. "State Dependence Can Explain the Risk Aversion Puzzle," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 973-1011, April.
    9. 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.
    10. Maria Grith & Wolfgang K. Härdle & Volker Krätschmer, 2017. "Reference-Dependent Preferences and the Empirical Pricing Kernel Puzzle," Review of Finance, European Finance Association, vol. 21(1), pages 269-298.
    11. Kiesel, Rüdiger & Rahe, Florentin, 2017. "Option pricing under time-varying risk-aversion with applications to risk forecasting," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 120-138.
    12. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    13. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    14. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    15. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    16. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    17. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 663-697, June.
    18. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    19. Yang Shen & Kun Fan & Tak Kuen Siu, 2014. "Option Valuation Under a Double Regime‐Switching Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(5), pages 451-478, May.
    20. Maria Grith & Wolfgang Karl Härdle & Volker Krätschmer, 2013. "Reference Dependent Preferences and the EPK Puzzle," SFB 649 Discussion Papers SFB649DP2013-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    21. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
    22. Majewski, Adam A. & Bormetti, Giacomo & Corsi, Fulvio, 2015. "Smile from the past: A general option pricing framework with multiple volatility and leverage components," Journal of Econometrics, Elsevier, vol. 187(2), pages 521-531.
    23. Geert Bekaert & Eric C. Engstrom & Nancy R. Xu, 2022. "The Time Variation in Risk Appetite and Uncertainty," Management Science, INFORMS, vol. 68(6), pages 3975-4004, June.
    24. Chen Tong & Zhuo Huang, 2021. "Pricing VIX options with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1180-1200, August.
    25. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    26. Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(1), pages 60-93, February.
    27. Chao‐Chun Chen & Ming‐Yang Hung, 2010. "Option pricing under Markov‐switching GARCH processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(5), pages 444-464, May.
    28. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    29. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    30. Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
    31. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.
    32. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    33. Hazem Daouk & Jie Qun Guo, 2004. "Switching asymmetric GARCH and options on a volatility index," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(3), pages 251-282, March.
    34. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    35. Zhuo Huang & Chen Tong & Tianyi Wang, 2019. "VIX term structure and VIX futures pricing with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 72-93, January.
    36. Robert J. Elliott & Tak Kuen Siu & Leunglung Chan, 2006. "Option Pricing For Garch Models With Markov Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 825-841.
    37. Li, George, 2007. "Time-varying risk aversion and asset prices," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 243-257, January.
    38. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    39. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, September.
    40. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    41. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    42. Zhuo Huang & Tianyi Wang & Peter Reinhard Hansen, 2017. "Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(4), pages 328-358, April.
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