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A Stochastic Volatility Model With Conditional Skewness

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  • Bruno Feunou
  • Roméo Tédongap

Abstract

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.

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  • Bruno Feunou & Roméo Tédongap, 2012. "A Stochastic Volatility Model With Conditional Skewness," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 576-591, July.
    • Handle: RePEc:taf:jnlbes:v:30:y:2012:i:4:p:576-591
    DOI: 10.1080/07350015.2012.715958
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    1. Junni L. Zhang & Wolfgang Karl Hardle & Cathy Y. Chen & Elisabeth Bommes, 2020. "Distillation of News Flow into Analysis of Stock Reactions," Papers 2009.10392, arXiv.org.
    2. Cheng, Ai-Ru & Jahan-Parvar, Mohammad R., 2014. "Risk–return trade-off in the pacific basin equity markets," Emerging Markets Review, Elsevier, vol. 18(C), pages 123-140.
    3. Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.
    4. Lhuissier, Stéphane, 2022. "Financial conditions and macroeconomic downside risks in the euro area," European Economic Review, Elsevier, vol. 143(C).
    5. Lin, Chu-Hsiung & Changchien, Chang-Cheng & Kao, Tzu-Chuan & Kao, Wei-Shun, 2014. "High-order moments and extreme value approach for value-at-risk," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 421-434.
    6. Mukhoti, Sujay, 2014. "Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness," MPRA Paper 62532, University Library of Munich, Germany.
    7. Stéphane Lhuissier, 2019. "Bayesian Inference for Markov-switching Skewed Autoregressive Models," Working papers 726, Banque de France.
    8. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    9. Javed Farrukh & Podgórski Krzysztof, 2014. "Leverage Effect for Volatility with Generalized Laplace Error," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 157-166, December.
    10. Hongkai Cao & Alexandru Badescu & Zhenyu Cui & Sarath Kumar Jayaraman, 2020. "Valuation of VIX and target volatility options with affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(12), pages 1880-1917, December.
    11. Sujay K Mukhoti, "undated". "Dynamic Feedback Effect And Skewness In Non-Stationary Stochastic Volatility Model With Leverage," Working papers 145, Indian Institute of Management Kozhikode.
    12. Iseringhausen, Martin, 2020. "The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 275-292.
    13. Max Wornowizki & Roland Fried & Simos G. Meintanis, 2017. "Fourier methods for analyzing piecewise constant volatilities," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 289-308, July.
    14. Junni L. Zhang & Wolfgang K. Härdle & Cathy Y. Chen & Elisabeth Bommes, 2015. "Distillation of News Flow into Analysis of Stock Reactions," SFB 649 Discussion Papers SFB649DP2015-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Maria Grith & Wolfgang K. Härdle & Alois Kneip & Heiko Wagner, 2016. "Functional Principal Component Analysis for Derivatives of Multivariate Curves," SFB 649 Discussion Papers SFB649DP2016-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Han, Hyojin & Khrapov, Stanislav & Renault, Eric, 2020. "The leverage effect puzzle revisited: Identification in discrete time," Journal of Econometrics, Elsevier, vol. 217(2), pages 230-258.
    17. Bruno Feunou & Cédric Okou, 2018. "Risk‐neutral moment‐based estimation of affine option pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 1007-1025, November.
    18. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    19. Bruno Feunou, 2023. "Generalized Autoregressive Gamma Processes," Staff Working Papers 23-40, Bank of Canada.
    20. Lo, Chien-Ling & Shih, Pai-Ta & Wang, Yaw-Huei & Yu, Min-Teh, 2019. "VIX derivatives: Valuation models and empirical evidence," Pacific-Basin Finance Journal, Elsevier, vol. 53(C), pages 1-21.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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