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Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods

Author

Listed:
  • Shuang Xiao

    (School of Management, Huazhong University of Science and Technology, Wuhan, P. R. China)

  • Guo Li

    (Center for Energy & Environmental Policy Research, Beijing Institute of Technology, Beijing, P. R. China3School of Management and Economics, Beijing Institute of Technology, Beijing, P. R. China)

  • Yunjing Jia

    (School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P. R. China)

Abstract

The constant elasticity of variance (CEV) model is widely studied and applied for volatility forecasting and optimal decision making in both areas of financial engineering and operational management, especially in option pricing, due to its good fitting effect for the volatility process of various assets such as stocks and commodities. However, it is extremely difficult to conduct parameter estimation for the CEV model in practice since the precise likelihood function cannot be derived. Motivated by the gap between theory and practice, this paper initiatively applies the Markov Chain-Monte Carlo (MCMC) method into parameter estimation for the CEV model. We first construct a theoretical structure on how to implement the MCMC method into the CEV model, and then execute an empirical analysis with big data of CSI 300 index collected from the Chinese stock market. The final empirical results reveal insights on two aspects: On one aspect, the simulated results of the convergence test are convergent, which demonstrates that the MCMC estimation method for the CEV model is effective; On the other aspect, by a comparison with other two most frequently used estimation methods, the maximum likelihood estimation (MLE) and the generalized moment estimation (GMM), our method is proved to be of high accuracy and has a simpler implementation and wider application.

Suggested Citation

  • Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:01:n:s0217595917400097
    DOI: 10.1142/S0217595917400097
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    as
    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Min Pan & Shengqiao Tang, 2011. "Option Pricing And Executive Stock Option Incentives: An Empirical Investigation Under General Error Distribution Stochastic Volatility Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(01), pages 81-93.
    3. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    4. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
    5. Kun Wu & Weixing Wu, 2016. "Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 14(2), pages 167-178, December.
    6. Li, Minqiang & Pearson, Neil D. & Poteshman, Allen M., 2004. "Conditional estimation of diffusion processes," Journal of Financial Economics, Elsevier, vol. 74(1), pages 31-66, October.
    7. Manuela Larguinho & José Carlos Dias & Carlos A. Braumann, 2013. "On the computation of option prices and Greeks under the CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 907-917, May.
    8. Junfeng Dong & Ye Shi & Liang Liang, 2014. "Futures and Option Contracts of the Supply Chain Influenced by e-Business Market," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-22.
    9. Jan Kallsen & Johannes Muhle-Karbe, 2015. "Option Pricing And Hedging With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 25(4), pages 702-723, October.
    10. Episcopos, Athanasios, 2000. "Further evidence on alternative continuous time models of the short-term interest rate," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(2), pages 199-212, June.
    11. Majewski, Adam A. & Bormetti, Giacomo & Corsi, Fulvio, 2015. "Smile from the past: A general option pricing framework with multiple volatility and leverage components," Journal of Econometrics, Elsevier, vol. 187(2), pages 521-531.
    12. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    13. Darrell Duffie & Peter Glynn, 2004. "Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals," Econometrica, Econometric Society, vol. 72(6), pages 1773-1808, November.
    14. 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.
    15. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    16. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    17. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    18. Chin-Tsai Lin & Cheng-Ru Wu, 2004. "Real Options: Batch Process And Market Entry/Exit Decisions Under Uncertainty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 35-52.
    19. Marcos Escobar & Pablo Olivares, 2011. "Risk Management Under A Factor Stochastic Volatility Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(01), pages 65-80.
    20. Stein, Jeremy, 1989. " Overreactions in the Options Market," Journal of Finance, American Finance Association, vol. 44(4), pages 1011-1023, September.
    21. 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.
    22. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    23. Haresh Gurnani & Mehmet Gümüş & Saibal Ray & Tridip Ray, 2012. "Optimal Procurement Strategy Under Supply Risk," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-31.
    24. 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.
    25. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-191, April.
    26. Jie Xu & Edward Huang & Chun-Hung Chen & Loo Hay Lee, 2015. "Simulation Optimization: A Review and Exploration in the New Era of Cloud Computing and Big Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-34.
    27. Xinhong Lu & Ken-Ichi Kawai & Koichi Maekawa, 2010. "Estimating Bivariate Garch-Jump Model Based On High Frequency Data: The Case Of Revaluation Of The Chinese Yuan In July 2005," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(02), pages 287-300.
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