淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1406200714484100
中文論文名稱 隱含波動率曲面變動之預測分析-利用台指選擇權之實證
英文論文名稱 Predictable Dynamics in the TAIEX Option Implied Volatility Surface
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 95
學期 2
出版年 96
研究生中文姓名 黃泰霖
研究生英文姓名 Tie-Lin Huang
學號 694490482
學位類別 碩士
語文別 中文
口試日期 2007-05-27
論文頁數 68頁
口試委員 指導教授-謝文良
委員-李進生
委員-林允永
委員-鐘惠民
中文關鍵字 隱含波動率  隱含波動率曲面  向量自我迴歸模型  隱含波動微笑 
英文關鍵字 implied volatility surface  implied volatility function  implied volatileity smile  option pricing 
學科別分類 學科別社會科學商學
中文摘要 本研究的主要目的為探討隱含波動率曲面是否具有可預測的效果,參照Goccalves and Guidolin (2006)所使用的VAR兩階段預測方式,對台指選擇權進行實證。

首先對每日在市場交易的選擇權之隱含波動率配適平滑公式,以價性、
到期期間為解釋變數,隱含波動率為被解釋變數,利用簡單迴歸估計出平滑公式的係數,並將所求出來的係數代入VAR模型對迴歸係數做預測,再利用修正過的迴歸係數做為更新平滑公式的係數,並且對隱含波動率曲面做預測,探討相同的預測方式在台指選擇權是否依然具有預測的效果。

實證結果發現,利用平滑公式配適隱含波動率所得到的係數,會隨著時間變動而變化,具有隨狀態時間改變的性質。利用二階段的預測方式,可以增加橫斷面模型對隱含波動率曲面的配適效果,隱含波動率曲面具有可預測性;然而隨著預測的期間增加,預測曲面的效果會迅速降低,甚至產生對係數過度配適的問題。
英文摘要 One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time.
In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the TAIEX option IVS. In the first stage we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas et al. (1998). In the second-stage we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models.
We find that not only the TAIEX implied volatility surface can be success fully modeled, but also that its movements over time are predictable in a statistical sense. However, when the fitted implied volatileity surface one week later, the VAR-type model’s prediction errors grow larger than another. The time passing is an important cause of overfitting at the movements of IVS.
論文目次 目錄
第一章 緒論
第一節 研究背景與動機......................................1
第二節 研究目的............................................3
第三節 研究架構與流程......................................4
第二章 文獻回顧
第一節 影響波動率曲面的因素................................6
第二節 波動率曲面配適與預測之相關文獻.....................11
第三章 研究方法
第一節 配適隱含波動率曲面之平滑公式.......................18
第二節 隱含波動率曲面參數之預測...........................28
第三節 利用橫斷面的平滑公式預測隱含波動率.................34
第四節 預測績效分析.......................................36
第四章 實證結果分析
第一節 資料來源與處理.....................................37
第二節 配適隱含波動率曲面.................................42
第三節 預測隱含波動率曲面.................................49
第四節 隱含波動率曲面之預測分析...........................51
第五章 結論與建議
結論......................................................62
對後續研究之建議..........................................63
參考文獻..................................................65



表次目錄

表3-1:存續期間(交易日)分類表.............................24
表3-2:價位分類表.........................................26
表4-1:隱含波動率隨到期期間、價內程度之基本統計表.........41
表4-2:隱含波動率曲面參數之基本統計量. ...................43
表4-3:隱含波動率曲面參數原始序列單根檢定結果.............50
表4-4:VAR模型最適落階期選取表............................50
表4-5:簡單平滑公式配適樣本內誤差衡量表...................54
表4-6:不同模型下的預測誤差衡量表(預測第1期)..............54
表4-7:不同模型下的預測誤差衡量表(預測第5期)..............54
表4-8:不同價性、到期期間之隱含波動率預測誤差衡量表(預測第1期).....57
表4-9:不同價性、到期期間之市場價格預測誤差衡量表(預測第1期).....58
表4-10:不同價性、到期期間之隱含波動率預測誤差衡量表(預測第5期).....59
表4-11:不同價性、到期期間之市場價格預測誤差衡量表(預測第5期).....60










圖次目錄

圖1-1:研究架構圖..........................................4
圖3-1:波動率曲面圖模擬圖.................................22
圖3-2:delta價性分類與K/S-1價性分類關係圖.................27
圖4-1a:台指選擇權成交量比較圖(買權) .....................38
圖4-1b:台指選擇權成交量比較圖(賣權) .....................38
圖4-2:平均每日合約數目分布圖(交易量高於50筆) ............39
圖4-3:樣本觀察值分布圖...................................40
圖4-4:利用簡單迴歸估計平滑公式係數之時間序列圖...........45
圖4-5:迴歸係數之自我相關圖...............................45
圖4-6:迴歸係數之交叉相關圖...............................46
圖4-7:曲面係數配適之斷面圖...............................48
圖4-8:利用簡單迴歸估計平滑公式係數之時間序列圖(20個交易日觀察值)..52
圖4-9:隱含波動率曲面圖...................................61

參考文獻 杜化宇 (Anthony H. Tu) 任紀為 (Chi-Wei Jen),外匯選擇權的定價與馬可夫鏈蒙地卡羅法的應用,風險管理學報 第七卷 第三期 2005年 11月

林莞菁、林丙輝(2003), 隱含波動率曲面變動因子-以台灣指數選擇權為例 ,台灣科技大學 : 財務金融研究所碩士論文

Bakshi G., C., Cao and Z., Chen, (1997), .“Empirical Performance of Alternative Option Pricing Models.”, Journal of Finance, 52, 2003-2049.

Bates, D. S. (1996). “Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options.” Review of Financial Studies, Vol. 9, pp.69-108.

Black, F., and M., Scholes, (1973), .“The Pricing of Options and Corporate Liabilities., Journal of Political Economy”, 81, 637-654.

Bollen, N.P., and R. E. Whaley (2004) , “Does net buying pressure affect the shape of implied volatility function?,” Journal of Finance, 59, pp.711-753.

Bollen, N.P.B., S. F. Gray, and R.E. Whaley, (2000) “Regime-Switching in Foreign Exchange Rates: Evidence from Currency Option Prices.” ,Journal of Econometrics, Vol.94, 239-276.

Bollerslev,T.,(1986) “Generalized Autoregressive Conditional Heteroscedasticity, ” Journal of Econometrics, Vol.31, 307-327.

Brandt, Michael W., and Tao Wu,(2002),“ Cross-Sectional Tests of Deterministic Volatility Functions”, Journal of. Empirical Finance 9, 525-550. 18

Campa, J., and K., Chang, (1995), “Testing the Expectations Hypothesis on the Term Structure of Volatilities.”, Journal of Finance, 50, 529-547.

Canina, L., and S., Figlewski, (1993), “The Informational Content of Implied Volatility.” Review of Financial Studies, 6, 659-681.

Christensen, B., and N., Prabhala, (1998), .“The Relation between Implied and Realized Volatility.”, Journal of Financial Economics, 50, 125-150.

Christoffersen, P., and C., Jacobs, (2004), .“The Importance of the Loss Function in Option Valua-tion.”, Journal of Financial Economics, 72, 291-318.

Cox, J. C. and Ross, S.A. (1976) “The Valuation of Options for Alternative Stochastic Processes”, Journal of Financial Economics, Vol.3, 145-166.

Cox,J.C.,S.A.Ross and M.Rubinstein,(1985),“Option Pricing:A Simplified of Interest Rates.”. Econometrica,Vol.53,No.2,March,385-407.

Das, S., Sundaram, R.,(1999) .“Of Smiles and Smirks:A Term Structure Prespective.” Journal of Financial and Quantitative Analysis 34, 211–239.

David, A., and P., Veronesi, (2002), .“Option Prices with Uncertain Fundamentals: Theory and Evidence on the Dynamics of Implied Volatilities.”, mimeo, University of Chicago.

Day, T., and C., Lewis, (1988), .“The Behavior of the Volatility Implicit in the Prices of Stock Index Options.,” Journal of Financial Economics, 22, 103-122.

Day, T., and C., Lewis, (1992), .“Stock Market Volatility and the Information Content of Stock Index Options.”, Journal of Econometrics, 52, 267-287.

Derman, E. and Kani, I. (1994) , “ The Volatility Smile and Its Implied Tree. ”, RISK, 7,139-145, 32-39.

Diebold, F., and C. Li,( 2003), .“Forecasting the Term Structure of Government Bond Yields.”, mimeo, University of Pennsylvania.

Diebold, F. and R., Mariano, (1995), .“Comparing Predictive Accuracy.”, Journal of Business and Economic Statistics, 13, 253-263.

Dumas, B., J. Fleming and R., Whaley, (1998), .“Implied Volatility Functions: Empirical Tests”. ,Journal of Finance, 53, 2059-2106.

Dupire, B. (1994). “Pricing with a smile, ” Risk 7: 18-20

Duque, J., and P. (1999), Teixeira Lopes, “Maturity and Volatility Effects on Smiles. Or Dying Smiling ? ”, Paper presented at EFA.

Engle, R., and V., Ng, (1993), .“Measuring and Testing the Impact of News on Volatility.”, Journal of Finance, 48, 1749-1778.

Fleming, J., (1998), “The Quality of Market Volatility Forecasts Implied by S&P 100 Index Option Prices.”, Journal of Empirical Finance, 5, 317-345.

Garcia, R., R., Luger, and E., Renault, (2003), .“Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables,”. Journal of Econometrics, 116, 49-83.

Garcia, R., E., Ghysels and E., Renault, (2003), .“The Econometrics of Option Pricing., forthcoming in Handbook of Financial Econometrics”, Y., A¨õt-Sahalia and L., P., Hansen (eds.), Elsevier-North Holland, Amsterdam.

Goncalves, S., and M., Guidolin (2006),“Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface.” Journal of Business,vol. 79,no. 3.

Heston, Steven, and Saikat Nandi.( 2000),“ A closed-form GARCH option valuation model.” Review of Financial Studies 13:585-625.

Hull, J., White, A.,(1987). “The pricing of options on assets with stochastic volatilities.” Journal of Finance,42, 281–300.

Martens, M., Zein, J., (2004). “Predicting financial volatility: High-frequency time-series forecasts vis-a`-vis implied volatility. ”Journal of Futures Markets, forthcoming.

Ncube,M..(1996),“Modeling implied volatility with OLS and panel data models.” Journal of Banking &Finance,20,71-84.

Nelson, C. R., Siegel, A. F. (1987), “Parsimonious Modeling of Yield Curves”, Journal of Business, Vol. 60, pp. 473-489.

Pena, Ignacio, Gonzalo Rubio, and Gregorio Serna. (1999). “Why do we smile? On the determinants of the implied volatility function.” Journal of Banking and Finance 23:1151-79.

Rosenberg, Joshua, and Robert Engle.,(2002).“ Empirical pricing kernels”. Journal of Financial Economics 64:341-72.

Rubinstein, M.(1976).“ The valuation of uncertain income streams and the pricing of options.” Bell Journal of Economics 7:407-25.

Rubinstein, M. (1985). “Nonparametric tests of alternative option pricing models using all reported traders and quotes on the 30 most active CBOE options classes from August 23, 1976 through August 31, 1978.” Journal of Finance, Vol. 40, pp.455-480.

Rubinstein, M. (1994) "Implied binomial trees," Journal of Finance, 49, pp.771-818.

Sheikh and Aamir M., (1991), “Transaction Data Tests of S&P 100 Call Option Pricing”, Journal of Financial and Quantitative Analysis 26, No. 4, pp.459-475.

Xu, X. and S. J. Taylor,. (1994) ,“The Term Structure of Volatility Implied by Foreign Exchange Options.”, Journal of Financial and Quantitative Analysis, Vol. 29, 57-74.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2009-07-16公開。
  • 同意授權瀏覽/列印電子全文服務,於2009-07-16起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信