著名的Black-Scholes 訂價公式是根據幾何布朗運動而來，用來計算歐式選擇權價格。幾何布朗運動要能正確，關鍵在於未來價格的變動與之前的價格是獨立的。我們以1997年7月2日到2004年12月31日的台灣股價加權指數，來檢查是否符合幾何布朗運動。另外，我們提出一個符合資料又合適的新模式，並採取Monte Carlo模擬法在(a)未來的價格變動與過去相似。(b)假設風險中立評價原則，計算台灣股票加權指數選擇權的價格。

　The celebrated Black-Scholes formula for European option pricing is based on geometric Brownian motion for the asset price movements. For a geometric Brownian motion to be accurate, a key premise is that future price changes are independent of past price movements. We examine real data to see if they are consistent with the geometric Brownian motion model and analyze the sequence of daily closing values of Taiwan Weight Stock Index from July 2, 1997 to December 31, 2004. Besides, we propose a new model that is consistent with the data as well as plausible and we use the technique of Monte Carlo simulation to obtain TAIEX option price under (a) the assumption that the future resembles the past and (b) a risk-neutral valuation based on the proposed model.

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