隨著金融商品日新月異，許多新興衍生性商品都是自己沒有接觸或研究過的，此時，衍生性商品的定價就成為很重要的議題，早期大部分的學者及投資人都使用Black-Scholes Model(BSM)及二項樹等傳統型評價模型來定價，而其中很多假設可能不太符合真實情況，不過也提供一個評價標準給我們。近年來，越來越多學者透過仿生法或生物演算法等新穎的演算法套用在衍生性商品評價，嘗試得到更精確的商品價值。此篇論文欲透過粒子群演算來評價選擇權，而粒子群演算法是人類觀察鳥類覓食的行為而發展出來的演算法，並多用於解決最佳化的問題。粒子群演算法的優點是能夠同時計算兩個變數(此篇為股價及時間)，運用在美式選擇權的評價則更加有效率，也可用來計算歐式選擇權，也能改善傳統模型的一些缺點。

In this ever-changing world, there are a lot of new derivatives which we never learn or know. Therefore, the pricing of derivatives has became an important issue. Most early scholars and investors used traditional evaluation models such as Black-Scholes model (BSM) and the Binomial Trees to price derivatives, many assumptions or applications of which may not be true, but also provide a standard for us. In recent years, more and more scholars have tried to obtain more accurate commodity values through novel algorithms such as bio-inspired or biological algorithms. This paper would like to evaluate the option by particle swarm optimization, and the particle swarm optimization is an algorithm developed by the behavior of birds foraging and is used to solve optimization problems. The advantage of particle swarm optimization is that it can calculate two variables at the same time (stock price and time.) and make the evaluation of American option more efficient, PSO can also be used to calculate European options and can also improve some of the shortcomings of the traditional model.

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