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姓名 江亮青(Liang-qing Jiang) 查詢紙本館藏 畢業系所 統計研究所 論文名稱 資產不對稱性波動參數的誤差估計與探討
(The Error Estimation and Discussion of AsymmetricalVolatility's Parameters of Asset)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 由於標的資產很容易受到外來資訊的影響，因而有時標的資產的價格在短期間內會呈現大幅上升或下跌的情形， 並導致標的資產的不對稱性波動(Volatility)。本文的主旨便在於先將實際資料裡的參數代入 TGARCH (1,1) 波動參數模型來模擬並獲得其標的資產在不對稱性波動之下的價格和報酬率資料。之後，利用 Black-Scholes 選擇權定價模型來獲得在該條件底下的選擇權價格資料。藉由蒙地卡羅模擬法 (Monte Carlo simulation)、最大概似估計法(Maximum Likelihood Estimation) 與本研究主要的三種做法分別求出 TGARCH(1,1) 模型的估計參數與實際參數之間誤差絕對值的平均、標準差 和均方誤差 (MSE，meansquare error)。最後再根據選擇權當中常見的三種情形 ─ 價平、價內和價外來進行上述參數的誤差推估與討論。
摘要(英) Because a financial asset is affected by outside information easily, sometimes the price of a financial asset has ascent or descent largely in short period. And it results in asymmetrical volatility of a financial asset. The purpose of this thesis is to simulate stock price and return rate of this financial asset in asymmetrical volatility by the method which is that parameters of real data substitute for TGARCH (1,1) model first. And then we predict value of option in the same situation by Black-Scholes option pricing model. Then, we estimate the absolute value of error, standard deviation, and mean square error between true and estimated parameters of TGARCH (1,1) model by Monte Carlo Simulation, Maximum Likelihood Estimation and three methods which is mentioned by this thesis. Finally, we estimate and discuss the error of foregoing parameters with three types of options ─ at-the-money, in-the-money and out-the-money.
關鍵字(中) ★ 最大概似估計法
★ 蒙地卡羅模擬法
★ Black-Scholes 選擇權定價模型
★ TGARCH模型
★ 不對稱性波動關鍵字(英) ★ Maximum Likelihood Estimation
★ Monte Carlo Simulation
★ TGARCH model
★ Black-Scholes option pricing model
★ Asymmetrical volatility論文目次 誌謝…………………………………………………………………… i
中文摘要 …………………………………………………………… iii
英文摘要 ………………………………………………………… iv
目錄 ………………………………………………………………… v
表目錄 …………………………………………………………… vii
第一章 緒論 ………………………………………………………… 1
1.1 研究背景與動機………………………………………………… 1
1.2 文獻回顧 ……………………………………………………… 2
第二章 模型介紹 …………………………………………………… 5
2.1 Black-Scholes 模型 ………………………………………… 5
2.2 ARCH 和 GARCH 模型 ………………………………………… 8
2.2.1 ARCH 模型 …………………………………………………… 9
2.2.2 GARCH 模型 ………………………………………………… 10
2.3 TGARCH 模型 ………………………………………………… 10
第三章 研究方法 ………………………………………………… 14
3.1 蒙地卡羅模擬法 ……………………………………………… 14
3.2 最大概似估計法 ……………………………………………… 15
3.2.1 以股價來反推參數 ………………………………………… 16
3.2.2 以股價和選擇權價格來反推參數(沒有估計誤差項)…… 18
3.2.3 以股價和選擇權價格來反推參數(有估計誤差項) ……… 21
第四章 實證分析 ………………………………………………… 24
4.1 資料來源 ……………………………………………………… 24
4.2 資料分析 ……………………………………………………… 25
4.2.1 價平選擇權 ………………………………………………… 25
4.2.2 價內選擇權 ………………………………………………… 27
4.2.3 價外選擇權 ………………………………………………… 29
第五章 結論 ……………………………………………………… 32
參考文獻 …………………………………………………………… 33
附錄 ………………………………………………………………… 36
參考文獻 [1] Aït-sahalia Y., and Kimmel R. (2007),“Maximum Likelihood Estimation of Stochastic Volatility Models”, Journal of Financial Economics 83, 413-452.
[2] Black F., and Scholes M. (1973), “The Pricing of Options and Corporate Liabilities”, The Journal of Political Economy, Vol. 81, No. 3., 637-654.
[3] Bollerslev, T. (1986),“Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31, 307-327.
[4] Box, G. E. P., and Jenkins, G. M. (1970), Time Series Analysis Forecasting and Control, 2nd ed., Holden-Day, San Francisco.
[5] Christoffersen P., and Jacobs K. (2004), “Which GARCH Model for Option Valuation?”, Management Science 50, 1204–1221.
[6] Duan J.C. (1995), “The GARCH Option Pricing Model”, Mathematical Finance, Vol. 5, 13-32.
[7] Duan J.C., Gauthier G., Sasseville C., and Simonato J.G. (2004), “Approximating the GJR-GARCH and EGARCH Option Pricing Models Analytically”, 1-29.
[8] Engle, R. F. (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation”, Econometrica, 50, 987-1008.
[9] Eraker B. (2004), “Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices”, Journal of Finance 59, 1367-1403.
[10] Girard E., Rahman H., and Zaher T. (2001), “Intertemporal risk ─ return relationship in the Asian markets around the Asian crisis”, Financial Services Review 10, 249-272.
[11] Glasserman, P. (2003), Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York.
[12] Glosten, L., R., Jagannathan, R., and Runkle, D., E. (1993), “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on stocks”, Journaal of Finance, 5, 1779-1801.
[13] Lee S.W., and Bruce E. Hansen (1994), “Asymptotic Theory for the GARCH(1,1) Quasi-Maximum Likelihood Estimator”, Econometric Theory, vol. 10, No. 1, 29-52.
[14] Liu S.M. (1995), “Maximum Likelihood Estimation of a GARCH stable Model.”, Journal of Applied Econometrics, vol. 10, 273-285.
[15] Johannes M. (2006), “Optimal Filtering of Jump-Diffusions: Extracting Latent States from Asset Prices”, Forthcoming Review of Financial Studies.
[16] Jonathan E. Ingersoll, Jr. (2006), “The Subjective and Objective Evaluation ofIncentive Stock Options”, Journal of Business, vol. 79, no.2, 453-487.
[17] Nelson, D. B. (1991), “Conditional Heteroskedasticity in asset returns: A new approach”, Econometrica, 59, 347-370.
[18] Pan J. (2002), “The jump-risk premia implicit in options: evidence from an integrated time-series study”, Journal of Financial Economics 63, 3–50.
[19] Papageorgiou, A. and Traub, J. F. (1996), “Beating Monte Carlo”, Risk, 9(6), 63-65.
[20] Shreve S.E. (2004), Stochastic Calculus for finance II Continuous-Time Models, Springer, New York.
[21] Tsay R.S. (2005), Analysis of Financial Time Series Second Edition. Hoboken, N.J. : Wiley.
[22] Zakoian, J.M. (1994), “Threshold Heteroskedastic models”, Journal of Economic Dynamics Control, 18, 931-955.
指導教授 傅承德(Cheng-der Fuh) 審核日期 2009-6-29 推文 plurk
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