本論文研究幾何布朗運動下含相乘性跳動的模型。本文在Poisson 過程下，以反覆程序檢測跳動。最大概似法被用來估計跳動參數λ與跳動大小。反覆程序原理以Matlab 程式語言加以撰寫。由台灣實證研究得到Black-Scholes 理論值，市場價格與模擬價格。GBM加入跳動所得到的選擇權價格與Black-Scholes 理論值是有差異的。

　The purpose of this study was to examine the model of geometric Brownian motion with multiplicative jumps. An iterative procedure was proposed to detect the jumps which follow a Poisson process with rate of intensityλ. The maximum likelihood method was used to estimate the parameterλ and the jump size. The algorithm of this iterative procedure was implemented in Matlab. The theoretical Black-Scholes, the market, and the simulated option prices were obtained through the investigation of a Taiwanese empirical study. The inclusion of the jump in the GBM resulted in option prices different from the Black-Scholes prices.

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