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Equilibruim approach of asset pricing under Lévy process

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  • Fu, Jun
  • Yang, Hailiang

Abstract

This work considers the equilibrium approach of asset pricing for Lévy process. It derives the equity premium and pricing kernel analytically for the stock price process, obtains an equilibrium option pricing formula, and explains some empirical evidence such as the negative variance risk premium, implied volatility smirk, and negative skewness risk premium by comparing the physical and risk-neutral distributions of the log return. Different from most of the current studies in equilibrium pricing under jump diffusion models, this work models the underlying asset price as the exponential of a Lévy process and thus allows nearly an arbitrage distribution of the jump component.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:701-708
    DOI: 10.1016/j.ejor.2012.06.037
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    Cited by:

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    2. Wei Guo & Xinfeng Ruan & Sebastian A. Gehricke & Jin E. Zhang, 2023. "Term spreads of implied volatility smirk and variance risk premium," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 829-857, July.
    3. 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.
    4. Marta Giampietro & Massimo Guidolin & Manuela Pedio, 2015. "Can No-Arbitrage SDF Models with Regime Shifts Explain the Correlations Between Commodity, Stock, and Bond Returns?," BAFFI CAREFIN Working Papers 1619, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    5. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
    6. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    7. 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.
    8. 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.
    9. 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.
    10. Hu, Zhihao & Yang, Ben-Zhang & He, Xin-Jiang & Yue, Jia, 2024. "Equilibrium pricing of European crude oil options with stochastic behaviour and jump risks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 212-230.
    11. Xiaoyu Tan & Shenghong Li & Shuyi Wang, 2020. "Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    12. 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.

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