Study of the Effectiveness of Pricing for SSE 50ETF Option: Based on B-S-M Model and Monte Carlo Model

doi:10.12005/orms.2017.0199

Operations Research and Management Science ›› 2017, Vol. 26 ›› Issue (8): 157-166.DOI: 10.12005/orms.2017.0199

• Application Research • Previous Articles Next Articles

Study of the Effectiveness of Pricing for SSE 50ETF Option: Based on B-S-M Model and Monte Carlo Model

FANG Yan^1,2, ZHANG Yuan-xi¹, QIAO Ming-zhe¹

1.School of Finance, Shanghai University of International Business and Economics, Shanghai 201620, China;
2.School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Received:2015-09-23 Online:2017-08-25

上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟

方艳^1,2, 张元玺¹, 乔明哲¹

1.上海对外经贸大学金融管理学院,上海 201620;
2.上海财经大学统计与管理学院,上海 200433

作者简介:方艳(1975-),女,安徽黄山人,讲师、硕士生导师,研究方向:计量经济、数量经济和金融工程; 张元玺(1993-),山东聊城人,男,硕士研究生;乔明哲(1976-),男,安徽蚌埠人,副教授、硕士生导师,研究方向:技术经济及管理。
基金资助:
基金项目:国家自然科学基金资助项目(11501355,71203139);上海市浦江人才计划项目(14PJ1404100);上海市教育委员会科研创新项目(14ZS147,15ZZ090);国家社科基金重大项目(15ZDA058);教育部人文社会科学项目(15YJA790039);教育部留学回国人员科研启动基金;中国博士后科学基金第59批面上资助项目;台州市哲学社会科学项目(14GHZ01)

Abstract

Abstract: As the first pilot option product in China’s capital market, the pricing of Shanghai Stock Exchange(SSE)50ETF option is particularly important. In this paper, both Black-Scholes-Merton(B-S-M)method and Monte Carlo simulation method will be used for SSE 50ETF option pricing. The empirical analysis indicates that: 1, IGARCH model is better than the traditional GARCH model in characterizing the dynamic volatility for SSE 50ETF options return; 2, with 1000 simulation running, Monte Carlo simulation methods are consistently more efficient than B-S-M; furthermore, except for quasi-Monte-Carlo simulations with dual variable, all pricing obtained from other Monte Carlo methods are more accurate than the one from B-S-M; 3, both B-S-M method and Monte Carlo simulation method can accurately and effectively simulate the SSE 50ETF options pricing. This study will provide the essential reference and guidance for the development of future option pricing model.

Key words: black-scholes model, monte carlo, quasi monte carlo, shanghai 50ETF option, IGARCH

摘要： 上证50ETF期权作为中国资本市场上股票期权的第一个试点产品,其定价问题尤为重要。本文分别运用B-S-M期权定价模型和蒙特卡罗模拟方法对其定价进行实证研究,分析结果表明:1)IGARCH模型比传统的GARCH模型更能较好地拟合上证50ETF的波动率;2)当模拟次数为1000时,蒙特卡罗方法的效率一致地高于B-S-M模型,并且除了对偶变量技术的拟蒙特卡罗其他模型的精确度也都高于B-S-M模型;3)B-S-M模型和蒙特卡罗模拟方法都可以较为准确地、有效地模拟出上证50ETF期权价格。这些研究将为今后期权定价模型的发展和完善提供必要的参考和指引。

关键词: B-S-M模型, 蒙特卡罗模拟, 拟蒙特卡罗模拟, 上证50ETF期权, IGARCH模型

CLC Number:

F830.9

FANG Yan, ZHANG Yuan-xi, QIAO Ming-zhe. Study of the Effectiveness of Pricing for SSE 50ETF Option: Based on B-S-M Model and Monte Carlo Model[J]. Operations Research and Management Science, 2017, 26(8): 157-166.

方艳, 张元玺, 乔明哲. 上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟[J]. 运筹与管理, 2017, 26(8): 157-166.

References

[1] Itō K. On stochastic differential equations[M]. American Mathematical Society, 1951, 4: 1-51.
[2] Black F, Scholes M. The pricing of options and corporate liabilities[J]. The Journal of Political Economy, 1973: 637-654.
[3] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1-2): 125-144.
[4] Cox J C, Ross S A. The valuation of options for alternative stochastic processes[J]. Journal of Financial Economics, 1976, 3(1-2): 145-166.
[5] Boyle P P. Options: A monte carlo approach[J]. Journal of Financial Economics, 1977, 4(3): 323-338.
[6] Kemna A G Z, Vorst A C F. A pricing method for options based on average asset values[J]. Journal of Banking & Finance, 1990, 14(1): 113-129.
[7] Pellizzari P. Efficient Monte Carlo pricing of European options using mean value control variates[J]. Decisions in Economics and Finance, 2001, 24(2): 107-126.
[8] Glasserman P. Monte Carlo methods in financial engineering[M]. Springer Science & Business Media, 2003.
[9] Korn R, Zeytun S. Efficient basket Monte Carlo option pricing via a simple analytical approximation[J]. Journal of Computational and Applied Mathematics, 2013, 243: 48-59.
[10] Paskov S H, Traub J F. Faster valuation of financial derivatives[J]. The Journal of Portfolio Management, 1995, 22(1): 113-123.
[11] Joy C, Boyle P P, Tan K S. Quasi-monte carlo methods in numerical finance[J]. Management Science, 1996, 42(6): 926-938.
[12] Cranley R, Patterson T N L. Randomization of number theoretic methods for multiple integration[J]. SIAM Journal on Numerical Analysis, 1976, 13(6): 904-914.
[13] Boyle P, Broadie M, Glasserman P. Monte Carlo methods for security pricing[J]. Journal of Economic Dynamics and Control, 1997, 21(8): 1267-1321.
[14] Akesson F, Lehoczky J P. Path generation for quasi-monte carlo simulation of mortgage-backed securities[J]. Management Science, 2000, 46(9): 1171-1187.
[15] Hickernell F J, Lemieux C, Owen A B. Control variates for quasi-monte carlo[J]. Statistical Science, 2005, 20(1): 1-31.
[16] 张普,吴冲锋.基于非参数蒙特卡罗模拟的股票波动性价值研究[J].管理科学,2009,22(3):89-95.
[17] 张丽花,张卫国,徐文坤.美式障碍期权定价的总体最小二乘拟蒙特卡罗模拟方法[J].数理统计与管理,2013,32(5):923-930.
[18] Merton R C. Lifetime portfolio selection under uncertainty: the continuous-time case[J].The Review of Economics and Statistics, 1969: 247-257.
[19] Andersen T G, Bollerslev T. Heterogeneous information arrivals and return volatility dynamics: uncovering the long-run in high frequency returns[J]. The Journal of Finance, 1997, 52(3): 975-1005.
[20] Engle R F. Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of U.K. Inflation[J]. Econometrica, 1982, 50.
[21] Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31(3): 307-327.
[22] Brandt M W, Jones C S. Volatility forecasting with range-based EGARCH models[J]. Journal of Business & Economic Statistics, 2006, 24(4): 470-486.
[23] Hung J C, Lee M C, Liu H C. Estimation of value-at-risk for energy commodities via fat-tailed GARCH models[J]. Energy Economics, 2008, 30(3): 1173-1191.
[24] Fang Y, Liu L, Liu J Z. A dynamic double asymmetric copula generalized autoregressive conditional heteroskedasticity model: application to China’s and US stock market[J]. Journal of Applied Statistics, 2015, 42(2): 327-346.
[25] 郑振龙,黄薏舟.波动率预测:GARCH模型与隐含波动率[J].数量经济技术经济研究,2010:140-150.
[26] 朱信凯,韩磊,曾晨晨.信息与农产品价格波动:基于EGARCH模型的分析[J].管理世界,2012,(11):57-66.
[27] 吴恒煜,朱福敏,温金明.基于ARMA-GARCH调和稳态Levy过程的期权定价[J].系统工程理论与实践,2013,33(11):2721-2733.
[28] 李传乐.我国商业银行市场风险量化体系研究[J].金融发展研究,2009,(3):62-66.
[29] Jarque C M, Bera A K. A test for normality of observations and regression residuals[J]. International Statistical Review/Revue Internationale de Statistique, 1987: 163-172.
[30] Ljung G M, Box G E P. On a measure of lack of fit in time series models[J]. Biometrika, 1978, 65(2): 297-303.
[31] Dickey D A, Fuller W A. Distribution of the estimators for autoregressive time series with a unit root[J]. Journal of the American Statistical Association, 1979, 74(366a): 427-431.
[32] Phillips P C B, Perron P. Testing for a unit root in time series regression[J]. Biometrika, 1988, 75(2): 335-346.
[33] Kwiatkowski D, Phillips P C B, Schmidt P, et al. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?[J]. Journal of Econometrics, 1992, 54(1): 159-178.

Study of the Effectiveness of Pricing for SSE 50ETF Option: Based on B-S-M Model and Monte Carlo Model

上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟

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