利用B-S方程建構最適之模糊投資組合

Using B-S Equation to Construct an Optimal Fuzzy Portfolio

王宣茹(Hsuan-Ju Wang)

指導教授 ： 練光祐

中原大學/工學院/電機工程研究所/碩士(2007年)

https://doi.org/10.6840/cycu200700812

摘要

選擇權市場和現貨市場息息相關，由選擇權市場所觀察到的指標，除了個別代表的意義之外，結合在一起所能提供的隱含消息也不少，其中隱含波動率和未平倉量的搭配，可解讀出投資人對未來多空走勢的看法，而隱含波動率本身對未來股價波動的預測比起其它波動型態指標都要來的貼近，且隱含的資訊也很豐富。若搭配歷史波動率輔助觀察，可避免掉隱含波動率被高估或低估的情形。本研究利用模糊理論的特性，將這些指標間的關係描述數學化，決策出報酬率與風險的最佳調整值，以提高交易報酬率，避免交易上的損失。由實驗結果顯示本研究所建構的模糊投資組合明顯優於一般大眾所使用的Markowitz投資理論。

關鍵字

歷史波動率 ； 未平倉量 ； Black-Scholes偏微分方程 ； 隱含波動率 ； Markowitz投資組合定理 ； 模糊理論

並列摘要

The option market and the spot market are closely related. By observing the targets of the option market, besides the respective meanings, many implied messages can be obtained through examining the several targets. From the implied volatility and the open interest, the investors’ viewpoints of the stock prices fluctuation in the future can be interpreted. For the capability of the forecast of the volatility in stock price, the implied volatility is better than the other volatility indexes, and the implied information is also abundant. If the historical volatility is used to assist the forecast, the conditions of overestimation or underestimation of the implied volatility can be avoided. The characteristics of the fuzzy theory are adopted in this research. The relationship of those indexes will be described in mathematical model to choose the best adjustment value of the return and the risk. Thus, the exchange return can be raised to avoid the exchange cost. The experiment results show that the fuzzy portfolio constructed in this research is superior to the Markowitz portfolio theory adopted by the masses.

並列關鍵字

Implied Volatility ； Historical Volatility ； Open Interest ； Fuzzy Theory ； Black-Scholes Equation ； Markowitz Portfolio Theory

參考文獻

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[18] 許美滿，“衍生性市場創新、交易機制與隱含波動”，淡江大學財務金融學系， 2005。

[2] H.M. Markowitz, “Portfolio Selection,” Journal of Finance, Vol. 7, pp. 77-91, 1952.

[3] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, pp. 637-654, 1973.

[4] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, pp. 338-353, 1965.