結合灰關聯分析之模糊連續遺傳演算法對選擇權之評價

本研究結合灰關聯分析之模糊連續遺傳演算法，做為評價選擇權的另一工具。首先以灰色關聯分析找尋除了Black-Scholes評價模型之外足以影響選擇權價格的因素，再透過模糊數之運算將實數變數轉為模糊數，做為模糊連續遺傳演算法的輸入與輸出變數，尋找更精確的選擇權評價方法，最後再和Black-Scholes評價模式相互比較。在總體經濟面選擇：一個月定存利率、對美元匯率與臺灣加權股價指數變動率三個變數。在技術指標方面選擇：標的股票成交量、個股選擇權成交量、個股選擇權未平倉量以及五日RSI等四個變數，做為模糊連續遺傳演算法的輸入變數，實證結果，在加入由灰關聯分析，所篩選的變數後，模糊連續遺傳演算法的預測準確度高於Black-Scholes評價模型以及僅以Black-Scholes模型之變數為輸入變數的模糊連續遺傳演算法。

關鍵字

灰關聯分析；模糊連續遺傳演算法；選擇權評價

並列摘要

This paper aims to combine fuzzy continuous genetic algorithm (FCGA) of grey relational analysis as another tool for the option pricing. In the first place, except for the Black-Scholes pricing model, we used grey relational analysis to seek the variables that are the factors sufficient to influence option price. Then, through the fuzzy number calculation, the variables were transformed to the fuzzy numbers which were used as the input and output variables for fuzzy continuous genetic algorithm. This helps seek more precise method of the option pricing. Finally, the results were compared with Black-Scholes option pricing model. With regard to the selection from the macroeconomic perspective, there are three variables, i.e., the monthly deposit rate, the exchange rate for Taiwan dollars to US, and the change rate of Taiwan stock exchange weighted price index. Considering the selection from the technical index perspective, there are four variables-the underlying stock trade volume, individual stock option trade volume, individual stock open interest volume, and 5-day RSI-used as the input and output variables for fuzzy continuous genetic algorithm. The empirical results revealed that, after the addition of variables selected by grey relational analysis, the forecasting precision gained by fuzzy continuous genetic algorithm was higher than that gained by Black-Scholes option pricing model as well as by using only Black-Scholes model variables as input variables of fuzzy continuous genetic algorithm.