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| 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.
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[5] Eraker, B., 2004. Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404.
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[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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| 402301.pdf | 1932Kb | Adobe PDF2 | 67 | View/Open |
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