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標題: 波動率曲面在不同VIX水平之行為特徵
Characteristics of Implied Volatility Surface in Various VIX Levels
作者: 程鵬章
Cheng, Peng-Chang
關鍵字: 波動率曲面;;VIX;Volatility Skew
出版社: 高階經理人碩士在職專班
引用: Bollen, N.P.B., and Whaley, R.E., 2004,〝Does net buying pressure affect the shape of implied volatility functions ?〞Journal of Finance 59(2), 711–753. Carr, Peter, and Wu, Liuren, 2003,〝The finite moment log stable process and option pricing ,〞Journal of Finance 58(2), 753-777. Chadwick, S. , 2006 ,〝Can the VIX signal market direction ? 〞Derivatives Strategy [edocument]., [retrieved 25.5.2009]. Chance, Don M. , and Brooks, Rebert, 2008,〝An introduction to derivatives and risk managment, 〞Thomson south-western ,OH. Cont, R., and da Fonseca, J., 2002,〝Dynamics of implied volatility surfaces,〞Quantitative Finance 2(1), 45–60. Cont, R., and Kokholm, Thomas, 2009,〝Consistent pricing model for index options and volatility derivatives,〞Nordic Finance Network F-2009-05. Doran, J. S., Tarrant, B. C. and Peterson, D. R., 2007,〝Is there information in the volatility skew ?〞Journal of Futures Markets 27, 921-960. Dumas, B., Fleming, J., and Whaley, R.E. , 1998,〝Implied volatility functions: empirical tests,〞Journal of Finance 53(6), 2059–2106. Giot, P. , 2005,〝On the relationships between implied volatility indexes and stock index returns,〞Journal of Portfolio Management 31(3), 92-100. Gonçalves, S., and Guidolin, M., 2006,〝Predictable dynamics in the S&P 500 index options implied volatility surface,〞J. Bus. 79(3), 1591–1635. Hsu, S.D.H. and Murray, B.M., 2007, 〝On the volatility of volatility 〞, Physica A : Statistical Mechanics and its Applications (380), 366-376. Kang, J. , and Park, H.J. , 2008,〝The information content of net buying pressure: evidence from the KOSPI 200 index option market, 〞Journal of Financial Markets 11, 36-56. le Roux, M., 2006,〝A long-term model of the dynamics of the S&P500 implied volatility surfaces, 〞Working Paper, ING Institutional Markets. Matt Larsena, 2004 ,〝A hands on approach to volatility trading,〞Futures, 42-45, The H.W. Wilson Company WN: 0425203153005. Muzzioli, S., 2007,〝The relation between implied and realized volatility,〞CEFIN Working Paper (4). Whaley, R.E. , 2000,〝The investor fear gauge,〞Journal of Portfolio Management, Spring 2000, 12-17. Whaley, R.E. , 2009,〝Understanding the VIX,〞The Journal of Portfolio Management 35(3), 98-105. Zhang , Jin E. and Xiang, Yi, 2005,〝Implied Volatility Smirk,〞Grant CERG HKU1068/01H Working Paper .
VIX指數為市場對「標的物未來三十(日曆)天波動程度」的預期,VIX是一序列不同履約價格買權及賣權的平均行為。若不同履約價格對未來波動率有不同預期,則形成 Volatility Skew /Smile。本研究建議以「交易日」為時間軸,來建構波動率曲面 ( Implied Volatility Surface, IVS ),以利於了解 VIX 和 Volatility Skew 每日相對變化情形。
在IVS上,定性觀察「VIX等位線」(該線上的波動率與VIX值相等) 在不同VIX水平的行為模式,發現其與 VIX 本身水平無關,卻與標的指數振幅有關。隨後,計算 VIX等位線在Delta Moneyness 軸上投影座標相對於 Black-Scholes ATM 的偏離程度,並以 DLTvix 命名之。本研究認為,DLTvix可視為選擇權市場對標的指數未來三十(日曆)天報酬率的預期。對賣(買)權而言,DLTvix 為負(正);負(正)的越多,表示預期負(正)報酬越高。
計算 2006/12/01 至 2010/02/28 共802個交易日之 DLTvix 與 RT30(標的指數未來三十日曆天報酬率) ,並以OLS法進行廻歸分析。結果顯示, DLTvix 對 RT30 有統計上顯著的預測能力。因此,本研究主張,台股選擇權市場隱藏有資訊內涵,可據以預測標的指數報酬率。

VIX index is implied by the current prices of underlying index option and represents expected future market volatility over the next 30 calendar days. VIX can be thought of as a weighted average of implied volatilities for put/call options across a series of strikes. Volatility Skew/Smile phenomenon result from volatility expected discrepancies between various exercise prices. We adopt the trading time, but not the expiration time, as time axis in IVS construction, this is helpful to observe relative daily variations between VIX and volatility skew.
On this volatility contour plane, we observe characteristics of "VIX location line" (i.e. zero value relative with daily VIX index) in various VIX levels, and find out its flow path is independent of VIX level, but relate to underlying index variation. We then define DLTvix as Black-Scholes Delta deviation between ATM and VIX location line projection component along Delta moneyness axis. We state that DLTvix can be considered as option participators'expectation on underlying index return over the next 30 calendar days. For the put (call) option, DLTvix is negative (positive); and the lower (higher) value of DLTvix, represents the less (more) expected return.
We calculate DLTvix and RT30 (index return over the next 30 calendar days) from 2006/12/01 to 2010/02/28, a total of 802 trading days. These results computed by OLS regression model show that, DLTvix have statistically significant predictive power on RT30. Our findings contend that the information extracted from Taiwan option market, is able to forecast the movement of underlying index.
其他識別: U0005-2806201021212100
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