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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/111446
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/111446


    Title: 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
    Authors: 黃國展
    Huang, Kuo Chan
    Contributors: 林士貴
    翁久幸

    Lin, Shih Kuei
    Weng, Chiu Hsing

    黃國展
    Huang, Kuo Chan
    Keywords: 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
    Date: 2017
    Issue Date: 2017-07-31 10:57:21 (UTC+8)
    Abstract: 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.
    Reference: [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.
    Description: 碩士
    國立政治大學
    統計學系
    104354023
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0104354023
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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