這篇文章著重於將GARCH選擇權評價模型配適台灣股市資料。 本文章所採用段(1995)提出的GARCH選擇權評價模型。段利用模擬的方法求解出歐市選擇權的價格，本篇文章也採用模擬的方法並且延伸到美式選擇權的評價。一般而言，模擬法求解美式選擇權並不若歐式選擇權方便。 然而，Longstaff和Schwartz提出的最小平方法是一種簡單迅速的美式選擇權評價方法。所以本文章將模擬出股價後再採用最小平方法進行美式選擇權評價。使用最大概似法配適實際的觀測值可以估計出GARCH模型中的參數。在參數估計以後，進行股價模擬，最後便可以進行選擇權評價。歐式選擇權使用模擬法和Black-Scholes模型做比較，而美式選擇權則使用有限差分法和最小平方法做比較。

This article emphasizes on fitting GARCH option pricing model with Taiwan stock market. Duan’s(1995) NGARCH option pricing model is adopted. Duan solved the European option by simulation, this article follow the method and extents to pricing American option. In general, simulation approach is not convenient to solve American options as well as European options. However, the least-squares method proposed by Longstaff and Schwartz is a simple and powerful tool, so this article tests the method. The NGARCH model has parameters, and base on loglikelihood function, we fit the model with empirical observations to obtain parameters. Then we can simulate the stock prices, once stock prices are simulated, the option value can be priced. Since the article simulates the option, there should be the antithetic approaches instead of simulation. In practice, the Black-Schoels model is the benchmark for pricing European option, so this article compares the simulated European options with Black-Scholes. For American option, this article compares the simulated American options which are priced by least-squares method with trinomial tree (finite difference method).

1. Introduction……………………………………….1
2. GARCH Model……………………………………5
3. Loglikelihood Function…………………………...7
4. Simulation………………………………………...10
5. European Option Pricing………………………..16
6. American Option Pricing………………………..17
7. Empirical Analysis……………………………….23
8. Conclusion………………………………………...28

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