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Beyond Stochastic Volatility and Jumps in Returns and Volatility

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  • Garland Durham
  • Yang-Ho Park
Abstract
While a great deal of attention has been focused on stochastic volatility in stock returns, there is strong evidence suggesting that return distributions have time-varying skewness and kurtosis as well. Under the risk-neutral measure, for example, this can be observed from variation across time in the shape of Black--Scholes implied volatility smiles. This article investigates model characteristics that are consistent with variation in the shape of return distributions using a stochastic volatility model with a regime-switching feature to allow for random changes in the parameters governing volatility of volatility, leverage effect, and jump intensity. The analysis consists of two steps. First, the models are estimated using only information from observed returns and option-implied volatility. Standard model assessment tools indicate a strong preference in favor of the proposed models. Since the information from option-implied skewness and kurtosis is not used in fitting the models, it is available for diagnostic purposes. In the second step of the analysis, regressions of option-implied skewness and kurtosis on the filtered state variables (and some controls) suggest that the models have strong explanatory power for these characteristics.

Suggested Citation

  • Garland Durham & Yang-Ho Park, 2013. "Beyond Stochastic Volatility and Jumps in Returns and Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 107-121, January.
    • Handle: RePEc:taf:jnlbes:v:31:y:2013:i:1:p:107-121
    DOI: 10.1080/07350015.2013.747800
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    Citations

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    Cited by:

    1. Martha Carpinteyro & Francisco Venegas-Martínez & Alí Aali-Bujari, 2021. "Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    2. Calvet, Laurent E. & Fearnley, Marcus & Fisher, Adlai J. & Leippold, Markus, 2015. "What is beneath the surface? Option pricing with multifrequency latent states," Journal of Econometrics, Elsevier, vol. 187(2), pages 498-511.
    3. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    4. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.
    5. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    6. Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Bogdan, Dima & Ştefana Maria, Dima & Roxana, Ioan, 2022. "A Value-at-Risk forecastability indicator in the framework of a Generalized Autoregressive Score with “Asymmetric Laplace Distribution”," Finance Research Letters, Elsevier, vol. 45(C).
    8. Daniela Neykova & Marcos Escobar & Rudi Zagst, 2015. "Optimal investment in multidimensional Markov-modulated affine models," Annals of Finance, Springer, vol. 11(3), pages 503-530, November.
    9. Marcos Escobar & Daniela Neykova & Rudi Zagst, 2015. "Portfolio Optimization In Affine Models With Markov Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-46.
    10. Jahan-Parvar, Mohammad R. & Mohammadi, Hassan, 2013. "Risk and return in the Tehran stock exchange," The Quarterly Review of Economics and Finance, Elsevier, vol. 53(3), pages 238-256.
    11. Reyes-García, Nallely Jacqueline & Venegas-Martínez, Francisco & Cruz-Aké, Salvador, 2018. "Un análisis comparativo entre GARCH-M, EGARCH y PJ-RS-EV para modelar la volatilidad de Índice de precios y cotizaciones de la Bolsa Mexicana de Valores [A Comparative Analysis among GARCH-M, EGARC," MPRA Paper 84304, University Library of Munich, Germany.
    12. M. Escobar & D. Neykova & R. Zagst, 2017. "HARA utility maximization in a Markov-switching bond–stock market," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1715-1733, November.
    13. Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.

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