混和常態模型的區間估計在股票和選擇權資料

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陳彥辰(Chen-Yen Chen) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

混和常態模型的區間估計在股票和選擇權資料
(Interval estimation in Mixture Normal Model with stock and option data)

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摘要(中)

資產報酬分布相對常態分配一直以來存在峰度和偏態的差異，而混和常態模型擁有近似任何連續分配模型的特性，並能夠捕捉峰度、偏態和多模型財務時間資料。統計理論對於估計精準度的評估常常忽略模型選擇的重要性，本文藉由加入選擇權資料來討論模型選擇的問題。由選擇權定價公式可以知道選擇權價格和標的物價格存在特定關係，因此本文探討結合股票報酬資料和選擇權資料進行波動率估計，並利用拔薛法建立信賴區間來評斷估計精準度。我們藉由模擬來檢視聯合估計的表現，另外也將此方法運用在台灣金融市場。

摘要(英)

The distribution of returns on financial asset has been found to exhibit substantial leptokurtosis, in many cases, also skewness relative to normal distribution. One attractive property of the Mixture normal model is that it is flexible enough to accommodate various shapes of continuous distributions, and able to capture leptokurtic, skewed and multimodal characteristics of financial time series data. Statistical theory ignores model selection in assessing estimation accuracy. Here we try to add option data to discuss the problem of model selection. Finance theory shows that option prices depend on the underlying stocks’ prices, thus the two kinds of data are related. This paper explores the approach that combines both stock return data and option data to perform the statistical analysis of volatility and consider bootstrap methods for computing confidence interval to illustrate the accuracy between two data sources. A simulation study is conducted to check finite sample performances of the proposed joint estimation. We also have the empirical result in Taiwan finance market.

關鍵字(中)

★ 混和常態模型
★ 波動率估計
★ 信賴區間

關鍵字(英)

★ mixture normal model
★ volatility estimation
★ confience interval

論文目次

摘要 i
Abstract ii
誌謝 iii
1 Introduction 1
2 Mixture normal model 4
3 Methodology 6
3.1 Estimation by stock return data . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Estimation by combining stock return data and option data . . . . . . . . 7
3.3 Interval estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Simulation study 11
4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Empirical study 20
iv
5.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.2 Empirical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6 Conclusion 25
References 27

參考文獻

[1] Alexander, C., and Narayanan, S. Option pricing with normal mixture returns:
Modelling excess kurtosis and uncertanity in volatility. ResearchGate (2001).
[2] Blattberg, R. C., and Gonedes, N. J. A comparison of the stable and student
distributions as statistical models for stock prices. Journal of Bussiness 47(2) (1974),
244–280.
[3] Chernov, M., and Ghysels, E. A study towards a unifid approach to the joint
estimation of objective and risk neutral measures for the purpose of options valuation.
Journal of Financial Economics 56 (2000), 407–458.
[4] Christie, A. On information arrival and hypothesis testing in event studies. Working paper, University of Rochester (1983).
[5] Claeskens, G., and Hjort, N. L. The focussed information criterion. Journal
of American Statistical Association 98 (2003), 900–945.
[6] Clark, P. K. A subordinated stochastic process model with fiite variance for
speculative prices. Econometrica 41(1) (1973), 135–155.
[7] DiCiccio, T. J., and Efron, B. Bootstrap confience intervals. Statistical Science
11 (1996), 189–228.
[8] Efron, B. Estimation and accuracy after model selection. Journal of American
Statistical Association 109 (2014), 991–1007.
[9] Esch, D. N. Non-normality facts and fallacies. Journal of Investment Management
8 (2010), 49–61.
[10] Gridgeman, N. T. A comparison of two methods of analysis of mixtures of normal
distributions. 343–366.
[11] Hjort, N. L., and Claeskens, G. Frequentist model average estimators. Journal
of American Statistical Association 98 (2003), 879–899.
[12] Hu, F., and Zidek, J. V. The weighted likelihood. Canadian Journal of Statistics
30 (2002), 347–371.
[13] Kamaruzzaman, Z. A. Isa, Z., and Ismail, M. T. Analysis of malaysia stock
return using mixture of normal distributions. International Journal of Sciences:
Basic and Applied Research 23 (2015), 197–206.
[14] Kon, S. J. Models of stock returns - a comparison. Journal of Finance 39(1) (1984),
147–165.
[15] Neumann, M. Option pricing under the mixture of distributions hypothesis. Diskussionspapier (1998).
[16] Newcomb, S. A generalized theory of the combination of observations so as to
obtain the best result. Technometrics 12 (1963), 823–833.
[17] Ornthanalai, C. Levy jump risk: Evidence from options and returns. Journal of
Financial Economics 112 (2014), 69–90.
[18] Praetz, P. D. The distribution of share price. Journal of Bussiness 45(1) (1972),
49–55.
[19] Press, S. J. A compound events model for security prices. Journal of Business 40
(1967), 49–55.
[20] Ritchey, R. J. Mixtures of normal distributions and the implication for option
pricing. The University of Arizona (1981).
[21] Stein, C. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proceedings of the third Berkeley symposium on mathematical
statistics and probability (1956), 197–206.
[22] Tan, K., and Chu, M. Estimation of portfolio return and value at risk using a
class of gaussian mixture distributions. The International Journal of Business and
Finance Research 6 (2012), 97–107.
[23] Venkataraman, S. Value at risk for a mixture of normal distributions: The use
of quasi-bayesian estimation techniques. Economic Perspectives 21(2) (1997).
[24] Wang, J. Generating daily changes in market variables using a multivariate mixture of normal distributions. Proceedings of the 2001 Winter Simulation Conference
(2001), 283–289.
[25] Yu, C. L. Li, H., and Wells, M. T. Mcmc estimation of lévy jump models using
stock and option prices. Mathematical Finance 21 (2011), 383–422.

指導教授

傅承德

審核日期

2017-7-6

推文