IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v54y2016icp326-338.html
   My bibliography  Save this article

Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums

Author

Listed:
  • Ruan, Xinfeng
  • Zhu, Wenli
  • Huang, Jiexiang
  • Zhang, Jin E.

Abstract

In this paper, we extend Zhang, Zhao and Chang's (2012) production-based equilibrium asset pricing model from a jump diffusion setting to a Lévy process with stochastic volatility. This paper is a further extension of Fu and Yang (2012), which is under a Lévy process with a constant volatility. Using newly developed closed-form formulas of equity premium and pricing kernel, we are able to price Schouten's (2005) moment swaps analytically. Numerical results show that our pricing formula performs very well. Our model explains Zhao, Zhang and Chang's (2013) empirical observations on moment risk premiums.

Suggested Citation

  • Ruan, Xinfeng & Zhu, Wenli & Huang, Jiexiang & Zhang, Jin E., 2016. "Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums," Economic Modelling, Elsevier, vol. 54(C), pages 326-338.
    • Handle: RePEc:eee:ecmode:v:54:y:2016:i:c:p:326-338
    DOI: 10.1016/j.econmod.2015.12.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999315004265
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2015.12.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    3. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    4. Diego Amaya & Peter Christoffersen & Kris Jacobs & Aurelio Vasquez, 2011. "Do Realized Skewness and Kurtosis Predict the Cross-Section of Equity Returns?," CREATES Research Papers 2011-44, Department of Economics and Business Economics, Aarhus University.
    5. Fu, Jun & Yang, Hailiang, 2012. "Equilibruim approach of asset pricing under Lévy process," European Journal of Operational Research, Elsevier, vol. 223(3), pages 701-708.
    6. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    7. 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.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    11. Vasicek, Oldrich Alfons, 2005. "The economics of interest rates," Journal of Financial Economics, Elsevier, vol. 76(2), pages 293-307, May.
    12. Prat, Georges, 2013. "Equity risk premium and time horizon: What do the U.S. secular data say?," Economic Modelling, Elsevier, vol. 34(C), pages 76-88.
    13. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    14. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
    15. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Accounting for the impact of higher order moments in foreign equity option pricing model," Economic Modelling, Elsevier, vol. 28(4), pages 1726-1729, July.
    16. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, vol. 59(3), pages 1405-1440, June.
    17. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    18. Anthony Neuberger, 2012. "Realized Skewness," Review of Financial Studies, Society for Financial Studies, vol. 25(11), pages 3423-3455.
    19. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
    20. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
    21. Wim Schoutens, 2005. "Moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 525-530.
    22. Georges Prat, 2013. "Equity risk premia and time horizon : what do US secular data say?," Post-Print hal-01385867, HAL.
    23. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    24. Vasicek, Oldrich Alfons, 2013. "General equilibrium with heterogeneous participants and discrete consumption times," Journal of Financial Economics, Elsevier, vol. 108(3), pages 608-614.
    25. Haitao Li & Martin T. Wells & Cindy L. Yu, 2008. "A Bayesian Analysis of Return Dynamics with Lévy Jumps," Review of Financial Studies, Society for Financial Studies, vol. 21(5), pages 2345-2378, September.
    26. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    27. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    28. Huimin Zhao & Jin E. Zhang & Eric C. Chang, 2013. "The Relation between Physical and Risk-neutral Cumulants," International Review of Finance, International Review of Finance Ltd., vol. 13(3), pages 345-381, September.
    29. Fung, Ka Wai Terence & Lau, Chi Keung Marco & Chan, Kwok Ho, 2014. "The conditional equity premium, cross-sectional returns and stochastic volatility," Economic Modelling, Elsevier, vol. 38(C), pages 316-327.
    30. Wendong Zheng & Yue Kuen Kwok, 2014. "Closed Form Pricing Formulas For Discretely Sampled Generalized Variance Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 855-881, October.
    31. Bates, David S., 2012. "U.S. stock market crash risk, 1926–2010," Journal of Financial Economics, Elsevier, vol. 105(2), pages 229-259.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wenli Zhu & Xinfeng Ruan, 2019. "Pricing Swaps on Discrete Realized Higher Moments Under the Lévy Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 507-532, February.
    2. Lazar, Emese & Qi, Shuyuan, 2022. "Model risk in the over-the-counter market," European Journal of Operational Research, Elsevier, vol. 298(2), pages 769-784.
    3. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    4. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    5. Li, Kaifeng & Xia, Bobo & Guo, Zhaoxuan, 2021. "A consumption-based asset pricing model with disappointment aversion and uncertainty shocks," Economic Modelling, Elsevier, vol. 94(C), pages 235-243.
    6. Slim, Skander & Dahmene, Meriam & Boughrara, Adel, 2020. "How informative are variance risk premium and implied volatility for Value-at-Risk prediction? International evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 22-37.
    7. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    8. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.
    9. Liu, Zhangxin (Frank) & Faff, Robert, 2017. "Hitting SKEW for SIX," Economic Modelling, Elsevier, vol. 64(C), pages 449-464.
    10. Ruan, Xinfeng & Zhang, Jin E., 2018. "Equilibrium variance risk premium in a cost-free production economy," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 42-60.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenli Zhu & Xinfeng Ruan, 2019. "Pricing Swaps on Discrete Realized Higher Moments Under the Lévy Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 507-532, February.
    2. Ruan, Xinfeng & Zhang, Jin E., 2018. "Equilibrium variance risk premium in a cost-free production economy," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 42-60.
    3. Du Du & Dan Luo, 2019. "The Pricing of Jump Propagation: Evidence from Spot and Options Markets," Management Science, INFORMS, vol. 67(5), pages 2360-2387, May.
    4. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    5. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    6. 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.
    7. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    8. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    9. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    10. 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.
    11. Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.
    12. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    15. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2018. "Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 1-29.
    16. 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.
    17. Shackleton, Mark B. & Taylor, Stephen J. & Yu, Peng, 2010. "A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2678-2693, November.
    18. Jin E. Zhang & Eric C. Chang & Huimin Zhao, 2020. "Market Excess Returns, Variance and the Third Cumulant," International Review of Finance, International Review of Finance Ltd., vol. 20(3), pages 605-637, September.
    19. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.
    20. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:54:y:2016:i:c:p:326-338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.