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系統識別號 U0002-2406200814121400
中文論文名稱 無模型設定隱含波動度之誤差分析-以台股指數選擇權
英文論文名稱 Error analysis of Model-free Implied Volatility-use TXO
校院名稱 淡江大學
系所名稱(中) 財務金融學系碩士班
系所名稱(英) Department of Banking and Finance
學年度 96
學期 2
出版年 97
研究生中文姓名 林旅仲
研究生英文姓名 Lu-Chung Lin
學號 695530781
學位類別 碩士
語文別 中文
口試日期 2008-05-31
論文頁數 49頁
口試委員 指導教授-林允永
指導教授-李進生
委員-邱忠榮
委員-謝文良
委員-劉祥熹
中文關鍵字 無模型設定隱含波動度  Black-Scholes模型 
英文關鍵字 Model-free Implied Volatility  Black-Scholes model 
學科別分類 學科別社會科學商學
中文摘要 有鑒於目前市場大都以Black-Scholes隱含波動度作為探討波動度的主要工具,而根據Jiang and Tian(2005)在服從跳躍擴散過程(jump-diffusion process)下所提出的無模型設定隱含波動度(model-free implied volatility)的觀念,進一步探討無模型設定隱含波動度與Black-Scholes隱含波動度在台灣指數選擇權上的波動度的差異,並且了解樣本內,兩種隱含波動度以Black-Scholes反推出的估計選擇權價格與真實選擇權價格的差異。另外比較樣本外與樣本內兩種模型有無變化。
實證結果可發現兩種隱含波動度相關性相當高,但是在誤差分析時可發現明顯差別。另外可發現不論樣本內或樣本外,Black-Scholes模型有較小的價格誤差,無模型設定隱含波動度有較大且不好的價格誤差,但在無模型設定隱含波動度在樣本外的估計選擇權價格誤差不完全比樣本內差,而Black-Scholes模型則有是有完全樣本外比樣本內差。
英文摘要 In recent years, Black-Scholes Implied Volatility has become the most famous tool in volatility researching. According to the idea of model-free implied volatility with jump-diffusion process that proposed by Jiang and Tian(2005), I prefer to know the difference between model-free and Black-Scholes Implied Volatility in TXO. More further, I compare in sample performance of two implied volatilities using Black-Scholes option pricing formula. Otherwise, I would like to know how pricing error going between in sample and out–of–sample.
Although empirical result shows these two implied volatilities has high correlation, there are distinct discrepancy in error test. No mater in or out-of-sample, Black-Scholes model has better performance in error test. In error test, in sample of model-free model is not exactly better than out-of-sample. But, in sample of Black-Sholes model is exactly better than out of sample.
論文目次 目錄
第一章 緒論 - 1 -
1.1 研究背景 - 1 -
1.2 研究動機與重要性 - 2 -
1.3 研究目的 - 2 -
第二章 文獻回顧 - 4 -
2.1 各種波動率模型相關文獻 - 6 -
2.1.1 Black - Scholes Model - 6 -
2.1.2 跳躍-擴散模型(Jump Diffusion Model) - 7 -
2.1.3 定態波動率模型(Deterministic Volatility Model) - 7 -
2.1.4 隨機波動率模型(Stochastic Volatility Model) - 8 -
2.1.5 時間序列模型(Time Series Model) - 9 -
2.1.6 模型比較 - 10 -
2.2 未來波動率的預測及資訊分析文獻 - 10 -
2.2.1 隱含波動率VS.歷史波動率 - 10 -
2.2.2 隱含波動率VS.交易量 - 13 -
2.2.3 隱含波動率VS.ARCH、GARCH系列模型 - 13 -
2.2.4 隱含波動率VS.跳躍-擴散模型 - 15 -
第三章 研究方法 - 16 -
3.1 實證研究資料 - 16 -
3.1.1 台灣指數選擇權(TXO) - 16 -
3.1.2 資料篩選 - 18 -
3.2 無模型設定隱含波動度(Model-free Implied Volatility) - 21 -
3.2.1 無模型設定的隱含波動度推導 - 22 -
3.2.2 實務上的限制 - 24 -
3.2.3 擷取誤差(Truncation Errors) - 25 -
3.2.3 離散化誤差(Discretization error) - 26 -
3.2.4 曲面擬合法(Curve-fitting Method) - 27 -
3.2.5 無模型設定隱含波動度計算方式 - 28 -
3.3 誤差分析指標 - 30 -
第四章 隱含波動度與誤差分析 - 32 -
4.1 隱含波動度模型的圖形分析 - 32 -
4.2 誤差分析 - 34 -
4.3.1 樣本內誤差分析 - 35 -
4.3.2 樣本外誤差分析 - 39 -
第五章 結論與建議 - 44 -
第六章 參考文獻 - 46 -

表目錄
表3-1 台灣指數選擇權契約規格 22
表3-2 台指選擇權成交量 25
表3-3 選擇權契約分類方式 27
表4-1 MF模型與BS模型隱含波動度基本統計量 40
表4-2 樣本內近月份契約BS模型與MF模型誤差分析 43
表4-3 樣本內遠月份契約BS模型與MF模型誤差分析 44
表4-4 樣本內30天到期BS模型與MF模型誤差分析 45
表4-5 樣本外近月份契約在BS模型與MF模型誤差分析 46
表4-6 樣本外遠月份契約在BS模型與MF模型誤差分析 47
表4-7 樣本外30天到期BS模型與MF模型誤差分析 48
表4-8 30天到期BS模型樣本內、外誤差分析比較 49
表4-9 30天到期MF模型樣本內、外誤差分析比較 49

圖目錄
圖3-1 台指選擇權成交量 25
圖4-1 30天期無模型設定隱含波動度與B-S隱含波動度 39

參考文獻 王甡(1995),[報酬衝擊對條件波動所造成之不對稱效果 台灣股票市場之實證分析],證券市場發展季刊,7:1,125-160
Ait-Sahalia, Y., and A. W. Lo, 1998,”Nonparametric Estimation of State-price Densities Implicit in Financial Asset Prices,” Journal of Finance, 53, 499-547.
Andersen, Torben & Tim Bollerslev, 1998, “Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts,” International Economic Review, 39, 4, 885-905.
Bates, D. S., 1991, “The Crash of ‘87: What It Expected? The Evidence from Option Markets,” Journal of Finance, 46, 1009-1044.
Black, F., & Scholes, M., 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81, 637-659.
Blair, B. J., Poon, S. H., & Taylor, S. J., 2000, “Forecasting S&P100 Volatility: the Incremental Information Content of Implied Volatilities and High-frequency Index Returns,” Journal of Econometrics, 105, 5-26.
Bollerslev, Tim, 1986, “Generalized Autoregressive Conditional Heteroscedasticity,” Journal of Econometrics, 31, 307-327.
Bollerslev, Tim, Michael Gibson and Hao Zhou, 2005, “Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities”, Working paper, Department of Economics, Duke University, Division of Research and Statistics, Federal Reserve Board.
Breeden, D. T., and R. H. Litzenberger, 1978, “Prices of State-Contingent Claims Implicit in Option Prices,” Journal of Business, 51, 621-651.
Britten-Jones, M., & Neuberger, A., 2000, “Option Prices, Implied Price Processes, Stochastic Volatility,” Journal of Finance, 55, 2, 839-866.
Campa, J. M., K. P. Chang, and R. L. Reider, 1998, “Implied Exchange Rate Distributions: Evidence from OTC Option Markets,” Journal of International Money and Finance, 17, 117-160.
Chan, Kam C., L. Cheng, & P. P. Lung, 2004, “Net buying pressure, volatility smile, and abnormal profit of Hang Seng Index Options,” Journal of Futures Markets, 24, 1165-1194.
Christensen, B.J., & N.R. Prabhala, 1998, “The Relation Between Implied and Realized Volatility,” Journal of Financial Economics, 50, 125-150.
Cox, J.C. and S.A. Ross, 1976, “The Valuation of Options for Alternative Stochastic Processes,” Journal of Financial Economics, 3, 145-166.
Day, Ted E. & Craig M. Lewis., 1992, “Stock Market Volatility and the Information Content of stock Index Options,” Journal of Econometrics, 52, 267-287.
Derman, E., and I. Kani, 1994, “Riding on a smile,” Risk, 7, 32-39.
Derman, E., and I. Kani, 1998, “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility,” International Jounal of Theoretical and Applied Finance, 1, 61-110.
Dumas, B., J. Fleming, & R. Whaley, 1998, “Implied Volatility Functions: Empirical Tests,” Journal of finance, 53, 2059-2106.
Dupire, Bruno, 1994, “Pricing with a smile,” Risk 7, 18-20.
Dupire, Bruno, 1997, “Pricing and hedging with smiles; in Michael A H. Dempster and Staneley R. Pliska,” eds.: Mathematics of Derivative Securities.
Donaldson, G., & M. Kamstra, 2004, “Volatility Forecasts, Trading Volume, and the ARCH versus Option-Implied Volatility Trade-off, Federal Reserve Bank of Atlanta,” Working Paper Series, 1-41.
Ederington, L. H., & W. Guan, 2002, “Why are Those Options Smiling?,” Journal of Derivatives, 10, 2, 9-34.
Engle, Robert F., 1982, “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica,” 50, 4, 987-1007.
Engle, Robert F. & V. M. Ng, 1993, Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48, 1749-1788.
Fleming, Jeff, 1998, “The Quality of Market Volatility Forecasts Implied by S&P100 Index Option Prices, Journal of Empirical Finance,” 5, 4, 317-345
Glosten, L. R., Jagannathan, R.,& Runkle, D. E., 1993, “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,” Journal of Finance, 48, 1779-1801.
Hull, J., White, A., 1987, “The pricing of options on assets with stochastic volatilities,” Journal of Finance, 42,281-300.
Jackwerth, J. C., 1999, “Option-Implied Risk-Neutral Distributions and Implied Binomail Trees: A Literature Review,” Journal of Derivatives, 6, 1-17.
Jiang, G., J. and Y. S. Tian, 2005, “The Model-Free Implied Volatility and Its Information Content” The Review of Financial Studies, 18, 1306-1342.
Jorion, P., 1995, “Predicting Volatility in the Foreign Exchange Market,” Journal of Finance, 50, 507-528.
Joseph K. W. Fung, 2007, “The Information Content of Option Implied Volatility Surrounding the 1997 Hong Kong Stock Market Crash,” The Journal of Futures Markets, 27, No.6, 555-574.
Kim, I. J. and S. Kim(2004), “Empirical Comparison of Alternative Stochastic Volatility Option Pricing Models:Evidence from Korean KOSPI 200 index options market,” Pacific-Basin Finance Journal, Vol.12, pp.117-142.
Lamoureux, C. G., and W. D. Lastrapes, 1993, “Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities,” Review of Financial Studies, 6, 293-326.
Merton, R. C, 1976, “Option Pricing When the Underlying Stock Returns Are Discontinuous,”Journal of Financial Economics, 3, 125-144.
Poon, S. H., & Granger, C. W. J., 2003, “Forecasting Volatility in Financial Markets: A Review,” Journal of Economic Literature, 41, 2, 478-539.
Rubinstein, M., 1994, Implied Binomial Trees, Journal of Finance 49, 771-818.
Shimko, D., 1993, “Bounds of Probability,” Risk, 6, 33-37.
Torben G. Andersen & Oleg Bondarenko, 2007, “Construction and Interpretation of Model-Free Implied Volatility,” NBER Working Papers 13449, National Bureau of Economic Research, Inc.
Zhang, Benjamin Yibin, Hao Zhou, & Haibin Zhu, 2005, “Explaining Credit Default Swap Spreads with Equity Volatility and Jump Risks of Individual Firms,” Working Paper , Federal Reserve Board.
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