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Persistent and transient variance components in option pricing models with variance-dependent Kernel

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  • Ghanbari, Hamed

Abstract

This paper examines theoretically and empirically a variance-dependent pricing kernel in the continuous-time two-factor stochastic volatility (SV) model. We investigate the relevance of such a kernel in the joint modeling of index returns and option prices. We contrast the pricing performance of this model in capturing the term structure effects and smile/smirk patterns to discrete-time GARCH models with similar variance-dependent kernels. We find negative and significant risk premium for both volatility factors, implying that investors are willing to pay for insurance against increases in volatility risk, even if it has little persistence. In-sample, the component GARCH model exhibits a slightly better fit overall and across all maturity buckets than the two-factor SV model. However, the two-factor SV model reduces strike price bias, giving rise to the model’s ability in reconciling the physical and risk-neutral distribution. Out-of-sample, the two-factor SV model has better fit to data.

Suggested Citation

  • Ghanbari, Hamed, 2024. "Persistent and transient variance components in option pricing models with variance-dependent Kernel," Journal of Empirical Finance, Elsevier, vol. 79(C).
  • Handle: RePEc:eee:empfin:v:79:y:2024:i:c:s0927539824000665
    DOI: 10.1016/j.jempfin.2024.101531
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    as
    1. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    3. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    4. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    5. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    6. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    7. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    8. 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.
    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. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    11. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    12. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    13. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    14. Ewald, Christian & Zou, Yihan, 2021. "Stochastic volatility: A tale of co-jumps, non-normality, GMM and high frequency data," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 37-52.
    15. Jinji Hao & Jin E. Zhang, 2013. "GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 11(3), pages 556-580, June.
    16. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    17. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    18. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor, 2015. "The risk premia embedded in index options," Journal of Financial Economics, Elsevier, vol. 117(3), pages 558-584.
    19. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    20. Matthew Linn & Sophie Shive & Tyler Shumway, 2018. "Pricing Kernel Monotonicity and Conditional Information," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 493-531.
    21. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    22. 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.
    23. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    24. Fousseni Chabi-Yo, 2012. "Pricing Kernels with Stochastic Skewness and Volatility Risk," Management Science, INFORMS, vol. 58(3), pages 624-640, March.
    25. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    26. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
    27. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    28. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    29. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    30. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    31. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    32. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
    33. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    34. Jean-François Bégin & Christian Dorion & Geneviève Gauthier, 2020. "Idiosyncratic Jump Risk Matters: Evidence from Equity Returns and Options," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 155-211.
    35. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277.
    36. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    37. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    38. 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.
    39. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    40. 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.
    41. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    42. Pedro Santa-Clara & Shu Yan, 2010. "Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options," The Review of Economics and Statistics, MIT Press, vol. 92(2), pages 435-451, May.
    43. 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.
    44. Hamed Ghanbari & Michael Oancea & Stylianos Perrakis, 2021. "Shedding light on a dark matter: Jump diffusion and option‐implied investor preferences," European Financial Management, European Financial Management Association, vol. 27(2), pages 244-286, March.
    45. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    46. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    47. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    48. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    49. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    50. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
    51. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    52. 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.
    53. Corradi, Valentina, 2000. "Reconsidering the continuous time limit of the GARCH(1, 1) process," Journal of Econometrics, Elsevier, vol. 96(1), pages 145-153, May.
    54. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2020. "Affine multivariate GARCH models," Journal of Banking & Finance, Elsevier, vol. 118(C).
    55. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    56. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    57. 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.
    58. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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    More about this item

    Keywords

    Component GARCH; Joint estimations; Two-factor GARCH; Two-factor stochastic volatility; Variance-dependent pricing Kernel; Variance risk premium;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • 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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