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研究生:歐丞剛
研究生(外文):Cheng-gang Ou
論文名稱:實際波動度模型下的VIX選擇權定價
指導教授:楊曉文楊曉文引用關係
指導教授(外文):Sharon S. Yang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:財務金融學系
學門:商業及管理學門
學類:財務金融學類
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:32
中文關鍵詞:日內報酬波動度隨機波動度模型
外文關鍵詞:Realize VolatilityStochastic volatility modelHARGL model
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Corsi, Fusari, and Vecchia (2013)提出間斷的隨機波動度模型,Heterogeneous Autoregressive Gamma with Leverage (HARGL),此模型將市場的日內報酬波動度替代變數(Realize Volatility,RV)納入考量,並使用多因子過程來反應資料的長、中、短期的資訊,特別是在捕捉資料長記憶性的現象上,這是傳統方法上較無法被反應的部分。因此,本研究使用此模型來對VIX選擇權做定價,結果發現,在不考慮期間及價內外下, HARGL模型的定價效果都是優於GARCH模型,且此模型對於到期期間較長或深價內和深價外的選擇權定價效果更好。
In this paper, we use a discrete-time stochastic volatility option pricing model, Heterogeneous Autoregressive Gamma with Leverage (HARGL) model, which proposed by Corsi et al. (2013) to price the VIX options. This model uses the Realize Volatility (RV) as a proxy for the unobservable return volatility and proposes a both long-memory and multi-components process with a leverage effect. An empirical analysis of VIX index options illustrates that this model outperforms GARCH option pricing model, especially for longer expiration date, deep-in-the-money, and deep-out-of-the-money options.
摘 要 i
Abstract ii
目錄 iii
圖目錄 iv
表目錄 v
第一章 緒論 1
第二章 模型 5
2-1 報酬的動態假設 5
2-2 Realized volatility的動態過程 6
2-3 風險中立下的機率測度 7
2-4 比較模型 8
2-5 參數估計及結果 10
第三章 選擇權定價及結果 12
3-1 樣本描述 12
3-2 選擇權定價方法 15
3-3 選擇權定價結果 16
第四章 結論 23
參考文獻 24

參考文獻
﹝1﹞Merton, R. C. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of financial economics, 8(4), 323-361.
﹝2﹞Andersen, T. G., Bollerslev, T., Diebold, F. X., &; Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 61(1), 43-76.
﹝3﹞Andersen, T. G., Bollerslev, T., Diebold, F. X., &; Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579-625.
﹝4﹞Barndorff‐Nielsen, O. E., &; Shephard, N. (2001). Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 167-241.
﹝5﹞Barndorff‐Nielsen, O. E., &; Shephard, N. (2002). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17(5), 457-477.
﹝6﹞Barndorff-Nielsen, O. E., &; Shephard, N. (2005). How accurate is the asymptotic approximation to the distribution of realized variance. Identification and inference for econometric models. A Festschrift in honour of TJ Rothenberg, 306-311.
﹝7﹞Christoffersen, P., Feunou, B., Jacobs, K., &; Meddahi, N. (2012). The economic value of realized volatility: Using high-frequency returns for option valuation (No. 2012-34). Bank of Canada Working Paper.
﹝8﹞Li, G., &; Zhang, C. (2010). On the number of state variables in options pricing. Management Science, 56(11), 2058-2075.
﹝9﹞Adrian, T., &; Rosenberg, J. (2008). Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk. The Journal of Finance, 63(6), 2997-3030.
﹝10﹞Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7(2), 174-196.
﹝11﹞Corsi, F., Fusari, N., &; La Vecchia, D. (2013). Realizing smiles: Options pricing with realized volatility. Journal of Financial Economics, 107(2), 284-304.
﹝12﹞Cox, J. C., Ingersoll Jr, J. E., &; Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica: Journal of the Econometric Society, 385-407.
﹝13﹞Ané, T., &; Geman, H. (2000). Order flow, transaction clock, and normality of asset returns. The Journal of Finance, 55(5), 2259-2284.
﹝14﹞Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.
﹝15﹞Duan, J. C. (1995). The GARCH option pricing model. Mathematical finance, 5(1), 13-32.
﹝16﹞Gourieroux, C., &; Jasiak, J. (2006). Autoregressive gamma processes. Journal of Forecasting, 25(2), 129-152.

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