政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/111446
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  全文筆數/總筆數 : 109952/140891 (78%)
造訪人次 : 46243594      線上人數 : 1021
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜尋範圍 查詢小技巧：
  • 您可在西文檢索詞彙前後加上"雙引號"，以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋，建議至進階搜尋限定作者欄位，可獲得較完整資料
    •  進階搜尋
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/111446


    請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/111446


    題名: Lévy過程下Stochastic Volatility與Variance Gamma之模型估計與實證分析
    Estimation and Empirical Analysis of Stochastic Volatility Model and Variance Gamma Model under Lévy Processes
    作者: 黃國展
    Huang, Kuo Chan
    貢獻者: 林士貴
    翁久幸
    Lin, Shih Kuei
    Weng, Chiu Hsing
    黃國展
    Huang, Kuo Chan
    關鍵詞: 隨機波動度模型
    波動度聚集
    Lévy過程
    跳躍風險
    粒子濾波器
    Stochastic volatility model
    Volatility clustering
    Lévy-process
    Jump risk
    Particle filter
    日期: 2017
    上傳時間: 2017-07-31 10:57:21 (UTC+8)
    摘要: 本研究以Lévy過程為模型基礎，考慮Merton Jump及跳躍強度服從Hawkes Process的Merton Jump兩種跳躍風險，利用Particle Filter方法及EM演算法估計出模型參數並計算出對數概似值、AIC及BIC。以S&P500指數為實證資料，比較隨機波動度模型、Variance Gamma模型及兩種不同跳躍風險對市場真實價格的配適效果。實證結果顯示，隨機波動度模型其配適效果勝於Variance Gamma模型，且加入跳躍風險後可使模型配適效果提升，尤其在模型中加入跳躍強度服從Hawkes Process的Merton Jump，其配適效果更勝於Merton Jump。整體而言，本研究發現，以S&P500指數為實證資料時，SVHJ模型有較好的配適效果。
    This paper, based on the Lévy process, considers two kinds of jump risk, Merton Jump and the Merton Jump whose jump intensity follows Hawkes Process. We use Particle Filter method and EM Algorithm to estimate the model parameters and calculate the log-likelihood value, AIC and BIC. We collect the S&P500 index for our empirical analysis and then compare the goodness of fit between the stochastic volatility model, the Variance Gamma model and two different jump risks. The empirical results show that the stochastic volatility model is better than the Variance Gamma model, and it is better to consider the jump risk in the model, especially the Merton Jump whose jump intensity follows Hawkes Process. The goodness of fit is better than Merton Jump. Overall, we find SVHJ model has better goodness of fit when S&P500 index was used as the empirical data.
    參考文獻: [1] Bakshi, G., Cao, C., & Chen, Z. W., 1997. Empirical performance of alternative option pricing models. Journal of Finance, 52: 2003-2049.
    [2] Bates, D. S., 1996. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies, 9: 69-107.
    [3] Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31: 307-327.
    [4] Christoffersen, P., Jacobs, K., & Mimouni, K., 2010. Volatility dynamics for the S&P500: Evidence from realized volatility, daily returns, and option prices. Review of Financial Studies, 23: 3141-3189.
    [5] Eraker, B., 2004. Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404.
    [6] Heston, S. L., 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6: 327-343.
    [7] Hull, J., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2): 281-300.
    [8] Madan, D. B., Milne, F., 1991. Option Pricing With V.G. Martingale Components. Mathematical Finance, 1(4): 39–55.
    [9] Madan, D. B., Seneta, E., 1990. The variance gamma (V.G.) model for share market returns. Journal of Business, 63: 511-524.
    [10] Madan, D. B., Carr, P. P.,Chang, E.C., 1998. The variance gamma (V.G.) model for share market returns. European Finance Review ,2: 79–105.
    [11] Merton, R. C., 1976. Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 63: 3-50.
    [12] Ornthanalai, C., 2014. Lévy jump risk: Evidence from options and returns. Journal of Financial Economics, 112: 69-90.
    [13] Pitt, M., Shephard, N., 1999. Filtering via simulation based on auxiliaryparticle filters. J. Am. Stat. Assoc. 94: 590-599.
    [14] Pitt, M., 2002. Smooth particle filters for likelihood evaluation and maximization.Unpublished working paper. University of Warwick.
    描述: 碩士
    國立政治大學
    統計學系
    104354023
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0104354023
    資料類型: thesis
    顯示於類別:[統計學系] 學位論文

    文件中的檔案:

    檔案 大小格式瀏覽次數
    402301.pdf1932KbAdobe PDF265檢視/開啟


    在政大典藏中所有的資料項目都受到原著作權保護.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回饋