選擇權是一種常見的衍生性金融商品，在世界各地的金融市場交易非常活躍。也因應不同的客戶需求，進而衍生出各種不同交易方式的選擇權，亞式選擇權就是其中之一。亞式選擇權評價需計算未來資產價格之平均，使得亞式選擇權沒有封閉解。 許多資產價格報酬變動無法完全用幾何布朗運動解釋，若是出現重大新聞，資產價格即會急遽波動，Merton(1976)提出跳躍擴散模型解釋此現象。 本研究以股價變動符合跳躍擴散模型為基礎，導出亞式遠期生效選擇權解析近似公式，以蒙地卡羅法模擬的亞式選擇權為基準，判斷解析近似公式之準確度。 Options is a common financial derivatives products, and the transactions of options are active around the world. In response to different customers needs, and then derives a variety of different types of options, one of them is Asian options. It does not exist closed form for Arithmetic Asian options because the payoff of Asian options is determined by the average underlying price over some pre-set period of time. Changes in asset prices can not be explained entirely by geometric Brownian motions. Asset prices will fluctuate sharply if significant events occur. Jump-diffusion model proposed by Merton(1976) is explained this phenomenon. In this study we derive analytic approximation formulae for pricing strike Asian options contain Jump-diffusion model. We use Monte Carlo simulation approach as benchmark verifying the accuracy of our formulae.
