台指選擇權市場最適波動度指標之研究

A Research for the Optimal Volatility Index in TXO

10.30003/JRM.200707.0002

羅庚辛(Keng-Hsin Lo)；藍宇文(Yu-Wen Lan)；張尚原(Shan-Yuan Chang)

波動度指標 ； 不對稱關係 ； Volatility Index ； Asymmetric Relation

風險管理學報

9卷2期（2007 / 07 / 01）

123 - 147

繁體中文

芝加哥選擇權交易所（CBOE）於1993公布波動度指數（VXO），並在2003又推出修正波動度指數（VIX），說明了波動度指標的重要性與非唯一之特性。本文依研究目的：選取最適波動度指標、分析最適波動度指標與股價指數同期報酬及未來報酬關係、可否利用最適波動度指標來發展提高報酬的投資策略等進行分析。研究對象為2002/01/02至2006/03/31總計1,046筆之台灣集中市場加權股價指數（TAIEX）收盤價格日資料。研究方法利用七種不同波動度指標與真實波動度（RV）、TAIEX同期報酬、TAIEX未來報酬進行平均絕對誤差與迴歸等分析。研究發現，CBOE於1993推出的VXO，在解釋RV能力上優於2003年的VIX，也優於其他五項指標，是台指選擇權市場的最適波動度指標。此外VXO與TAIEX同期報酬呈現負向關係、與TAIEX未來報酬呈現低VXO水準時為顯著負報酬；高VXO水準時為顯著正報酬關係，說明投資者可利用VXO判斷TAIEX的可能走勢，進而形成可提高超額報酬機率之投資決策。

Whereas CBOE published the volatility index (VXO) in 1993 and declared the revision (VIX) in 2003, this event had exhibited us importance and non-solitary of such an index. We aimed to find out the optimal volatility index, the relationship between optimal volatility index and contemporaneous as well as future return of stock index and, to find out the way to exploit optimal volatility index for an optimal investment strategy. We utilized 1,046 daily closed data of TAIEX within period of 2002/01/02 to 2006/03/31. We also utilized seven kinds of volatility indices to clarify their relationship with real volatility (RV), contemporaneous as well as future return of TAIEX via the means of MAE, regression, etc. This study illustrates that VXO transcends VIX as well as other five remaining indices in explanning RV thus is recognized as the optimal index. We found also the negative relation between VXO and contemporaneous TAIEX return, as well as the tendency of low VXO brings up negative return and high VXO brings up positive return in the future. These facts imply that an investor may exploit VXO as a gauge of TAIEX to scheme an investment strategy with higher probability of excess profit.

1. 李存修、盧佳鈺、江木偉(2006)。台指選擇權隱含波動率指標之資訊內涵－新編VIX指標之實證。證券市場發展季刊，17(4)，1-42。
   連結：
2. Beckers, S.(1981).Standard Deviations Implied in Option Prices as Predictors of Future Stock Price Variability.Journal of Banking and Finance,5(3),363-382.
3. Black, F.,M. Scholes(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Econometrics,81(3),637-654.
4. Canina, L.,. Figlewski(1993).The Informational Content of Implied Volatility.The Review of Financial Studies,6(3),659-681.
5. Chiras, D.P.,S. Manaster(1978).The Information Content of Option Prices and a Test of Market Efficiency.Journal of Financial Economics,6(3),213-234.
6. Christensen, B.J.,N.R. Prabhala(1998).The Relation Between Implied and Realized Volatility.Journal of Financial Economics,50(2),125-150.
7. Chu, S.H.,S. Freund(1996).Volatility Estimation for Stock Index Option: GARCH Approach.The Quarterly Review of Economics and Finance,36(4),431-450.
8. Copeland, M.M.,T.E. Copeland(1999).Market Timing: Style and Size Rotation Using the VIX.Financial Analysts Journal,55(2),73-81.
9. Day, T.E.,C.M. Lewis(1988).The Behavior of the Volatility Implicit in the Price of Stock Index Option.Journal of Finance Economics,22(1),103-122.
10. Dickey, D.A.,W.A. Fuller(1979).Distribution of the Estimators for Autoregressive Time Series with a Unit Root.Journal of the American Statistical Association,74(366),427-431.
11. Dumas, B.,J. Fleming,R. Whaley(1998).Implied Volatility Functions: Empirical Tests.The Journal of Finance,53(6),2059-2106.
12. Figlewski, S.,X. Wang(2000).Working Paper S-00-37Working Paper S-00-37,New York University, Stern School of Business.
13. Fleming, J..The Rationality of Market Volatility Forecasts Implied by S&P100 Index Options.Duke University.
14. French, K.R.,G.W. Schwert,R.F. Stambaugh(1987).Expected Stock Returns and Volatility.Journal of Financial Economics,19(1),3-29.
15. Giot, P.(2005).Relationships between Implied Volatility Indexes and Stock Index Returns.Journal of Portfolio Management,31(3),92-100.
16. Giot, P.(2003).The Information Content of Implied Volatility Indexes for Forecasting Volatility and Market Risk.Journal of Futures Markets,23(5),441-454.
17. Granger, C.W.J.,P. Newbold(1974).Spurious Regressions in Econometrics.Journal of Econometrics,2(2),111-120.
18. Gwilym, O.A.(2001).Forcasting Volatility for Options Pricing for the U.K. Stock Market.Journal of Finanacial Management and Analysis,14(2),55-62.
19. Harvey, C.R.,R.E. Whaley(1991).S&P100 Index Option Volatility.The Journal of Finance,46(4),1551-1561.
20. Lamoureux, C.G.,W.D. Lastrapes(1993).Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatility.The Review of Financial Studies,6(2),293-326.
21. Latane, H.A.,R.J. Rendleman(1976).Standard Deviation of Stock Price Ratios Implied in Option Prices.The Journal of Finance,31(2),369-381.
22. Mayhew, S.,C. Stivers(2003).Stock Return Dynamics, Option Volume, and the Information Content of Implied Volatility.The Journal of Futures Markets,23(7),615-646.
23. Merton, R.C.(1973).Theory of Rational Option Pricing.Bell Journal of Economics and Management Science,4(1),141-183.
24. Poon, S.H.,W.J.C. Granger(2003).Forecasting Volatility in Financial Market: A Review.Journal of Economic Literature,41(2),478-539.
25. Said, S.E.,D.A. Dickey(1984).Testing for Unit Roots in ARMA Models of Unknown Order.Biometrica,71(3),599-607.
26. Schmalensee, R.,R.R. Trippi(1978).Common Stock Volatility Expectation by Option Premia.The Journal of Finance,33(1),129-147.
27. Schwert, G.W.(1989).Why Does Stock Market Volatility Change over Time?.The Journal of Finance,44(5),1115-1154.
28. Traub, H.,L. Ferreira,M. McArdle,M. Antognelli(2000).Fear and Greed in Global Asset Allocation.The Journal of Investing,9(1),21-37.
29. Vasilellis, G.A.,N. Meade(1996).Forecasting Volatility for Portfolio Selection.Journal of Business Finance and Accounting,23(1),125-143.
30. Whaley, R.E.(2000).The Investor Fear Gauge.Journal of Portfolio Management,26(3),12-17.
31. 李命志、趙其琳(2001)。波動性預測模型能力之比較－臺灣認購權證之實證研究。台灣銀行季刊，52(4)，101-127。