臺灣博碩士論文加值系統

Britten-Jones and Neuberger(2000)推導出當標的資產價格在服從擴散過程假設之下的無模型設定的隱含波動度模型。Jiang and Tian（2005）進一步的將無模型設定隱含波動度推廣，當標的資產價格在服從跳躍-擴散過程假設之下的無模型設定的隱含波動度模型。本文主要根據Jiang and Tian (2005)將無模型設定的隱含波動度應用在S&P500指數選擇權的方法，改以CBOE VIX White Paper (2009)計算VIX指數方式求算無模型設定的隱含波動度，並應用HJM模型反求隱含波動度，以觀察無模型設定的隱含波動度應用在利率選擇權上是否能有相同效果，而本文以歐洲美元期貨選擇權為研究對象檢驗隱含波動度的預測能力及其所包含的資訊，結果發現由歐洲美元期貨選擇權所算出的隱含波動度沒有Jiang and Tian (2005)使用S&P500指數選擇權的預測能力高，而無模型設定隱含波動度相對歷史波動度仍具有資訊效率性但無法包含所有HJM隱含波動度資訊，卻包含所有歷史波動度的資訊，且無模型設定隱含波動度相對HJM隱含波動度不具資訊效率性。而在考慮結構性轉變之後，HJM隱含波動度反而包含了未來波動度的重要資訊，且在結構性轉變後之HJM隱含波動度同時包含所有無模型設定隱含波動度資訊及歷史波動度的資訊。

Britten-Jones and Neuberger（2000）derived the model-free implied volatilities under the assumption that the price of underlying asset follows diffusion process. Jiang and Tian（2005）further extend the above model-free implied volatility to asset price process with jumps and develop a simple method for implementing the model-free implied volatility. This paper follows CBOE VIX White Paper (2009) calculated VIX as model-free implied volatilities instead of Jiang and Tian (2005) derived model-free implied volatilities from S&P500 index options. We want to know whether the model-free implied volatilities have the same effect in interest rate options or not? In addition, we perform a direct test of the informational efficiency of interest rate options market using model-free implied volatilities.
Our results from Eurodollar futures options suggest that model-free implied volatilities can not subsume all information contained in the HJM implied volatilities and are not more efficient forecast for future realized volatilities. However, model-free implied volatilities can subsume all information contained in past realized volatilities.
We further considered the structural breaks. After structural breaks HJM implied volatilities subsume all information contained in model-free implied volatilities and past realized volatilities and are more efficient forecast for future realized volatilities.

摘要 I
Abstract II
目錄 III
表目錄 IV
圖目錄 IV
第壹章 緒 論 1
第一節、研究動機 1
第二節、研究目的 5
第貳章 相關文獻探討 7
第一節、隱含波動度相關文獻 7
第二節、結構性轉變相關文獻 10
第參章 研究方法 12
第一節、無模型設定的隱含波動度 12
第二節、HJM隱含波動度 15
第三節、已實現波動度和歷史波動度 16
第四節、結構性轉變檢定 17
第肆章、實證結果分析 20
第一節、研究樣本與資料來源 20
第二節、樣本分析 21
第三節、隱含波動度的內含資訊 23
第四節、迴歸分析模型 24
第五節、波動度預測模型的實證分析 25
第六節、結構性轉變檢定之實證分析 33
第伍章、結論 39
參考文獻 41

1.楊奕農 (2006), 時間序列分析-經濟與財務上之應用, 台北：雙葉書廊

2.Andrews, D.W.K. (1993), “Test for parameter instability and structural change with unknown change point.” Econometrica 61, 821-856

3.Andrews, Donald W K and Ploberger, Werner, (1994), “Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative,” Econometrica, 62, 1383-1414

4.Amin, Kaushik I. , Andrew, J. Morton (1994), “Implied Volatility Functions inArbitrage-Free Term Structure Models” , Journal of Financial Economics, 35, pp.141-180.

5.Bai, J. and Perron, P. (1998), “Estimating and testing linear models with multiple structural changes.” Econometrica, 66: 47–78

6.Blair, B. J., S. Poon, and S. J. Taylor (2001), “Forecasting S&P100 Volatility: The Incremental Information Content of Implied Volatilities and High-frequency Index Retruns,” Journal of Econometrics, 105, 5-26.

7.Brace, A., D. Gatarek, and M. Musiela. (1997). “The market model of interest rate dynamics.” Mathematical Finance. 7, 127-155.

8.Britten-Jones, M., and A. Neuberger (2000), “Option Prices, Implied Price Processes, and Stochastic Volatility,” Journal of Finance, 55, 839–866.

9.Brown, Durbin, and Evans (1975), “Techniques for Testing the Constancy of Regression Relationships Over Time,” Journal of the Royal Statistical Society 37, 149-192

10.Cakici, Nusret., and Jintao Zhu. (2001), “Pricing Eurodollar Futures Options With The Heath-Jarrow-Morton Model,”. Journal of Futures Markets. Vol.21, No.7, 655-680.

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

12.Chiras, D. P., and M. Steven (1978), “The information content of option prices and a test of market efficiency.” Journal of Financial Economics, June-Sep,213-234.

13.Chow, Gregory C. (1960), “Tests of Equality Between Sets of Coefficients in Two Linear Regressions.” Econometrica. 28 , 591-605

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

15.Christiansen, Charlotte., and Charlotte Strunk, Hansen (2002), “Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model.” Review of Derivatives Research. 5, 51-80.

16.Cox, J. C., J. E. Ingersoll and S. A. Ross (1985), “A Theory of the Term Structure of Interest Rates’’, Econometrica, 53, 2, pp.385-407.

17.Day, T. E., and C. M. Lewis (1988), “The Behavior of the Volatility Implicity in the Price of Stock Index Option,” Journal of Finance Economics, 22, 103-122.

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

19.Engle, R. F. (1982), “Autoregressive conditional Heteroskedasticity with Estimates of The Variance of UK Inflation,” Econometrica, 50, 987-1008

20.Fitzgerald, D.(1999), “Trading Volatility,” Risk Management and Analysis. Vol.2: New Market and Products, Edited by C. Alexander, 261-291

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

22.Fleming, J., Ostdiek, B., and Whaley, R. E. (1995), “Predicting Stock Market. Volatility: A New Measure”, Journal of Futures Markets, Vol. 15, P265-302.

23.Hansen, Bruce E, (1997), “Approximate Asymptotic P Values for Structural-Change Tests,” Journal of Business and Economic Statistics, 15, 60-67

24.Hansen, B. E. (2001), “The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity.” Journal of Economic Perspectives, 15, 4, 117-128

25.Harvey, C. R., and R. E. Whaley (1991), “S&P 100 Index Option Volatility,” Journal of Finance, 46, 1551–1561.

26.Heath, D., R. Jarrow, and A. Morton. (1990).“Bond pricing and the term structure of interest rates: a discrete time approximation. ” The Journal of Financial and Quantitative Analysis. 25, 419-440.

27.Ho, T. S. Y. and S. B. Lee (1986), “Term Structure Movement and Pricing Interest Rate Contingent Claims’’, Journal of Finance, 41, 5, pp.1011-1029.

28.Hull, J. and A. White (1990), “Pricing Interest Rate Derivatives Securities’’, Review of Financial Studies, 3, 4, pp.573-592.

29.James A. Hyerczyk (2001), “Volatility Matters: Better Position Sizing,” Futures, May, 34-36.

30.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

31.Jorion, P. (1995), “Predicting Volatility in the Foreign Exchange Market,” Journal of Finance, 50, 507–528.

32.Joshi, Mark., and Riccardo Rebonato(2001), “A stochastic-volatility, displaced-diffusion extension of the LIBOR Market Model”, QUARC working paper

33.Kuo, I-Doun., and Dean Paxson. (2002). “Implied volatility functions for one and two-factor Health, Jarrow, and Morton models.” 現代財務論壇，台中東海大學。

34.Lamoureux, C. G. and W. D. Lastrapes (1993), “Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatility.” The Review of Financial Studies, 6(2), 293-326.

35.Latane, H. A., and R. J. Rendleman, Jr. (1976), “Standard Deviations of Stock Price Ratios Implied in Options Price,” Journal of Finance, 31,361-381

36.Liu, J., S. Wu, and J. V. Zidek (1997), “On segmented multivariate regressions”,. Statistica Sinica, 7, pp.497-525.

37.Longstaff, F. A. and E. S. Schwartz (1992), “Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model’’, Journal of Finance, 47, 4, pp. 1259-1282.

38.Low, Cheekiat (2000), “The fear and Exuberance from implied volatility of S&P100 Index Options,” Working Paper.

39.Poon S. H. and C. W. J. Granger (2003), “Forecasting Volatility in Financial Market : A Review,” Journal of Economic Literature, 41, 478-539

40.Quandt, Richard. (1960), “Tests of the Hypothesis that a Linear Regression Obeys Two Separate Regimes.” Journal of the American Statistical Association.55, 324-330

41.Rendleman, Jr., Richard, J., and Brit Bartter. (1980). “The Pricing of Options on Debt Securities.” Journal of Financial and Quantitative Analysis. 15(1), 11-24.

42.Vix White Paper (2009), “the powerful and flexible trading and risk management tool from the Chicago board options exchange” Chicago Board Options Exchange.

43.Whaley, R.E., (1981), "The investor fear gauge", Journal of Portfolio Management,vol.26, pp12-17.

44.Yao, Y. C. (1988). “Estimating the number of change-point via Schwarz' criterion.” Statistics & Probability Letters 6, 181-198.