學術產出-Theses
Article View/Open
Publication Export
-
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<br>翁久幸
Lin, Shih Kuei<br>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 31-Jul-2017 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 dc.contributor.advisor 林士貴<br>翁久幸 zh_TW dc.contributor.advisor Lin, Shih Kuei<br>Weng, Chiu Hsing en_US dc.contributor.author (Authors) 黃國展 zh_TW dc.contributor.author (Authors) Huang, Kuo Chan en_US dc.creator (作者) 黃國展 zh_TW dc.creator (作者) Huang, Kuo Chan en_US dc.date (日期) 2017 en_US dc.date.accessioned 31-Jul-2017 10:57:21 (UTC+8) - dc.date.available 31-Jul-2017 10:57:21 (UTC+8) - dc.date.issued (上傳時間) 31-Jul-2017 10:57:21 (UTC+8) - dc.identifier (Other Identifiers) G0104354023 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/111446 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 104354023 zh_TW dc.description.abstract (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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 第一章 緒論 11.1 研究動機 11.2 研究目的 2第二章 文獻回顧 32.1 Lévy Process 32.2 隨機波動度模型 32.3 Particles Filter 5第三章 研究方法 63.1 Lévy Process 63.2 報酬率模型 93.3 Particle Filter 133.4 Expectation-Maximization Algorithm 16第四章 實證分析 184.1 模擬分析 194.2 實證結果 19第五章 結論 22參考文獻 23附錄附錄 A：概似函數推導 25 zh_TW dc.format.extent 1979226 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0104354023 en_US dc.subject (關鍵詞) 隨機波動度模型 zh_TW dc.subject (關鍵詞) 波動度聚集 zh_TW dc.subject (關鍵詞) Lévy過程 zh_TW dc.subject (關鍵詞) 跳躍風險 zh_TW dc.subject (關鍵詞) 粒子濾波器 zh_TW dc.subject (關鍵詞) Stochastic volatility model en_US dc.subject (關鍵詞) Volatility clustering en_US dc.subject (關鍵詞) Lévy-process en_US dc.subject (關鍵詞) Jump risk en_US dc.subject (關鍵詞) Particle filter en_US dc.title (題名) Lévy過程下Stochastic Volatility與Variance Gamma之模型估計與實證分析 zh_TW dc.title (題名) Estimation and Empirical Analysis of Stochastic Volatility Model and Variance Gamma Model under Lévy Processes en_US dc.type (資料類型) thesis en_US dc.relation.reference (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. zh_TW
