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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/55000
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/55000


    Title: 跳躍相關風險下狀態轉換模型之選擇權定價:股價指數選擇權實證分析
    Option pricing of a stock index under regime switching model with dependent jump size risks: empirical analysis of the stock index option
    Authors: 林琮偉
    Lin, Tsung Wei
    Contributors: 劉惠美
    林士貴

    Liu, Hui Mei
    Lin, Shih Kuei

    林琮偉
    Lin, Tsung Wei
    Keywords: Esscher轉換
    跳躍相關風險下狀態轉換模型
    EM演算法
    概似比檢定
    敏感度分析
    定價誤差
    Esscher transformation
    regime switching model with dependent jump model
    EM algorithm
    likelihood ratio test
    sensitivity analysis
    pricing error
    Date: 2011
    Issue Date: 2012-10-30 14:36:13 (UTC+8)
    Abstract: 本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知,高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知,跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小,在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。
    In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error.
    Reference: 中文文獻
    [1] 汪昱頡,(2008)。跳躍風險下馬可夫轉換模型之實證分析,高雄大學統計研究所碩士論文。
    [2] 徐于琇,(2008)。跳躍風險下狀態轉換模型下SEM演算法及Gibbs Sampling之參數變異數估計,高雄大學統計研究所碩士論文。
    [3] 黃慈慧,(2011)。跳躍相關風險下狀態轉換模型之股價指數實證分析,國立政治大學統計學系碩士論文。
    英文文獻
    [4] Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society, Vol. 39, 1-38.
    [5] Duan, J. C., Popova, I., and Ritchken, P. (2002). “Option pricing under regime switching,” Quantitative Finance, Vol. 2, 116-132.
    [6] Elliott, R. J., Chan, L., and Siu, T. K., (2005). “Option pricing and Esscher transform under regime switching,” Annals of Finance, Vol. 1, 423-432.
    [7] Elliott, R. J., and Siu, T. K., (2012). “Option pricing and filtering with hidden Markov-modulated pure-jump processes,” Applied Mathematical Finance, iFirst, 1-25.
    [8] Gerber, H., and Shiu, E., (1994). “Option pricing by Esscher transforms,” Transactions of the Society of Actuaries, Vol. 46, 140.
    [9] Hamilton, J. D., (1989). “A new approach to the economic analysis of nonstationary time series and the business cycle,” Econometrica, Vol. 57, 357-384.
    [10] Hardy, M. R., (2001). “A regime-switching model of long-term stock returns,” North American Actuarial Journal, Vol. 5, 41-53.
    [11] Lange, K. A, (1995). “Gradient algorithm locally equivalent to the EM algorithm,” Journal of the Royal Statistical Society, Vol. 57, 425-437.
    [12] Liao, S. L., Chang, C. K., Lin, S. K., 2008, "A recursive formula of a participating contract embedding a surrender option," Journal of Financial Studies, Vol. 16, 107-147.
    [13] Liew, C. C., and Siu, T. K., (2010). “A hidden Markov regime-switching model for option valuation,” Insurance: Mathematics and Economics, Vol. 47, 374–384.
    [14] Lin, S. K., Lin, C. S., and Chou, C. Y., (2010). “A recursive formula of a participating contract embedding a surrender option under regime-switching model with jump risks: evidence from stock indices.” working paper.
    [15] Schaller, H., and Norden, S. V., (1997). “Regime switching in stock market returns,” Applied Financial Economics Vol. 7, 177-191.
    [16] Schwert, G. W., (1989). “Business Cycles, Financial Crises, and Stock Volatility,” Carnegie Rochester Conference Series on Public Policy, Vol. 31, 83-126.
    [17] Turner, C. M., Startz, R., and Nelson, C. R. (1989). “A Markov model of heteroscedasticity, risk and learning in the stock market,” Journal of Financial Economics, Vol. 25, 3-22.
    Description: 碩士
    國立政治大學
    統計研究所
    99354030
    100
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0099354030
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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