臺灣博碩士論文加值系統

本研究以台灣台指期加權指數2015年1月5日至2016年10月31日的選擇權資料，來計算其隱含波動程度與週選擇權之Theta值。
　　市場投資者除了利用B-S模型進行選擇權定價之外，亦可由市場交易價反推選擇權的隱含波動率，隱含波動率愈大代表市場投資人願意進行避險的心態與需求愈強烈。
　　在實證後發現VIX選擇權的隱含波動度其微笑波幅大致呈現出由左往右、由下往上的型式，且隱含波動度距離到期期間縮短而呈現逐步升高的趨勢，整體看來時間越長合約的隱含波動度越低。隨著到期期間縮短笑狀波幅之斜率會更加往上，意思是隨著到期時間的縮短，微笑狀波幅會呈現的相對陡峭。價內與價外的選擇權，其隱含波動程度差距也會擴大。
　　VIX指數選擇權，除了價內外程度之外，其到期期間的影響也相當值得重視。無論從樣本之配適或者從評價的成果看來，納入時間變數之後誤差都呈現相對的修正。表示期間因子對選擇權價的格評價之重要性很高，以到期期間和價內外程度作為變數因子之模型在整體評價上呈現出很高的經準度，且其評價模型的誤差也相對穩定，各年之中並無顯著之差異。

The study worked out the implied volatility and Theta value of weekly options based on the option data for weighted index number of Taiwan FITX from January 5, 2015 to October 31, 2016.
Apart from employing B-S model for the pricing of options, market investors could also reckon backwards from the market transaction prices to the implied volatility of options. The greater the implied volatility is, the stronger market investors’ mentality and requirements regarding the willingness of risk aversion will be.
The empirical study found that the volatility smile of implied volatility of VIX options generally presents a pattern extending from the lower left to the upper right and the implied volatility increases as the expiration period shorten. On average, the longer the contract is, the lower the implied volatility will be. With the expiration period getting shorter, the slope of the volatility smile increases, which means that the volatility smile will be steeper with the expiration date approaching and the gap of implied volatility between in the-money (ITM) options and out-of-the-money (OTM) options will increase.
Among the VIX options, the expiration date also plays a significantly important role besides the levels of ITM and OTM. Either from the fitness of samples or the evaluation results, errors are greatly improved after adding the factor of expiration date. It is critical to show the expiration date for evaluating of option prices. The maximum accuracy of evaluation will be achieved by taking the ITM and OTM levels and the expiration date as the models for explaining variables. Furthermore, the evaluation errors are fairly stable without any obvious gap among each year.

目錄 I
表目錄 II
圖目錄 III
第一章 緒論 1
第一節研究動機 1
第二節研究目的 3
第三節論文架構 4
第二章 文獻回顧 6
第一節選擇權 6
第二節Black and Scholes模型 8
第三節隱含波動率(Implied Volatility) 9
第四節VIX指數(Volatility Index) 11
第三章 研究方法 13
第一節資料來源 13
第二節週選擇權之介紹 14
第三節隱含波動率 15
第四節選擇權波動率指數 17
第四章 分析與結果 23
第一節隱含波動率 23
第二節臺指期週選擇權Theta值 28
第三節VIX選擇權隱含波動度 30
第四節估計模型 36
第五章 結論與建議 42
第一節研究結論 42
第二節研究建議 43
參考文獻 44

表目錄
表 2 2　選擇權買賣雙方之權利義務 7
表 4-1　2015-2016年每週星期一台指選擇權隱含波動率敘述統計 23
表 4-2　VIX選擇權敘述性統計 30
表 4-3　VIX買權隱含波動度分類敘述性統計 32
表 4-4　VIX賣權隱含波動度分類敘述性統計 33
表 4-5　各模型係數估計 37
表 4-6　各模型樣本內評價誤差 40

圖目錄
圖1-1　論文架構 5
圖4-1　2015-2016年每週一價外6%賣權隱含波動率與常態分佈比較 24
圖4-2　2015-2016年每週一價外4%賣權隱含波動率與常態分佈比較 24
圖4-3　2015-2016年每週一價外2%賣權隱含波動率與常態分佈比較 25
圖4-4　2015-2016年每週一價平賣權隱含波動率與常態分佈比較 25
圖4-5　2015-2016年每週一價內2%賣權隱含波動率與常態分佈比較 26
圖4-6　2015-2016年每週一價內4%賣權隱含波動率與常態分佈比較 26
圖4-7　2015-2016年每週一價內6%賣權隱含波動率與常態分佈比較 27
圖4-8　理論Theta與履約價格圖 28
圖4-9　臺指期週選擇權Theta值與買權履約價格圖 29
圖4-10 臺指期週選擇權Theta值與到期日的變化 29
圖4-11 VIX選擇權隱含波動度平面(低於30天) 33
圖4-12　VIX選擇權隱含波動度平面(30-60天) 33
圖4-13　VIX選擇權隱含波動度平面(60-90天) 34
圖4-14　VIX選擇權隱含波動度平面(90天以上) 34
圖4-15 不同合約之隱含波動度 37
圖4-16　相同合約在不同到期期間的隱含波動度 37
圖4-17　迴歸曲線右移 41
 

1.Black F. and Scholes M., (1973), “The pricing of options and corporate liabilities,” Journal of Political Economy, 81, 637-654.
2.Bollerslev, T., Chou, R. Y., & Kroner, K. F. (1992). ARCH modelling in finance: A review of theory and empirical evidence. Journal of Econometrics, 52, 5-59.
3.Boscaljon, B., G. Filbeck, and X. Zhao (2011), “Market timing using the VIX for style rotation,” Financial Services Review, 20, 35-44.
4.Copeland, M. M.,and T. E. Copeland,(1999), "Market timing: Style and size rotation using the VIX",. Financial Analysts Journal 55, 73-81
5.Cox J. C., Ross S. A., and Rubinstein M., (1979) “Option pricing: A simplified approach”, Journal of Financial Economics, 7, 229-263.
6.Edward Szado. (2009). “ VIX Futures and Options - A Case Study of Portfolio Diversification During the 2008 Financial Crisis. Journal of Alternative Investment.
7.Feinstein, S. P. (1989), “Forecasting Stock Market Volatility Using Options on Index Futures,” Economic Review, Federal Reserve Bank of Atlanta,74, 12-30.
8.Fleming et al., 1995 S. Fleming, S. Green, J. Hall Analysis and alleviation of male infertility Microsc Anal, 35 (1995),37–39
9.Jones, R., (2001), “Analyzing credit lines with fluctuating credit quality,” Working paper, Simon Fraser University.
10.MacBeth, J. D., & Merville, L. J. (1979), “An empirical examination of the Black-Scholes call option pricing model,” Journal of Finance, 35, 285-301.
11.Poon, S. and C. Granger (2003), “Forecasting Volatility in Financial Markets: A Review,” Journal of Economic Literature, 41(2), 478-539.
12.Qadan, M. and G. Cohen (2011) , “Is It Profitable to Invest According to the VIX Fear Index,” Journal of Modern Accounting and Auditing, 7:1, 86-90.
13.Rosenberg V. (2000), “Implied Volatility Functions: A Reprise” Journal of Derivatives , 7, No. 3, 51-64
14.Rubinstein, M. (1985), Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from 23 August, 1976 through 31 August, 1978. Journal of Finance, 40, 455-480.
15.Sarwar, G. (2012), “Is VIX an investor fear gauge in BRIC equity markets?” Journal of Multinational Financial Management , 22:3, 55-65.
16.Simon, D. P. and R. A. Wiggins (2001), “S&P Futures Returns and Contrary Sentiment Indicators,” Journal of Futures Market, 21:5, 447-462.
17.Skiadopoulos, G. and G. Konstantinidi (2011), “Are VIX futures prices predictable? An empirical investigation,” International Journal of Forecasting, 27, 543-560
18.Tompkins, J. A., and Tompkins, J. (1995), The Genesis Enterprise: CreatingPeak-to-peak Performance. New York: McGraw-Hill.
19.Whaley, R. E. (2000), “The Investor Fear Gauge,” The Journal of Portfolio Management, 12-17.