本論文主要是將鄭德鴻(2005)發展選擇權評價分析系統擴展加入隨機微分方程式的模擬及參數估計。我們修改原評價分析系統的使用介面，讓一般使用者更容易使用，而且新增了一些隨機模型與評價及估計方法，使整個系統能更加地完整，也更便於使用。此評價分析系統分為三大部分：一是選擇權評價分析系統，二是標的資產價格模擬分析系統，最後是模型參數估計系統。最後，我們利用網路的資料進行實證分析，比較本系統方法所得到的價格與真實市場價格間的差異。

In this thesis, we expand the option pricing and virtual asset model system by Cheng (2005) and include new simulations and maximum likelihood estimation of the parameter of the stochastic differential equations. For easy manipulation of general users, the interface of original option pricing system is modified. In addition, in order to let the system more completely, some stochastic models and methods of pricing and estimation are added. This system can be divided into three major parts. One is an
option pricing system; The second is an asset model simulation system; The last is estimation system of the parameter of the model. Finally, the analysis for the data of network are carried out. The differences of the prices between estimator of this system and real market are compared.

1 前言 1
2 評價模型與模型參數估計方法 2
2.1 跳躍擴散評價模型 .......................... 2
2.2 常數彈性波動參數估計模型(CEV) ............. 3
2.3 最大概似估計法(MLE) ....................... 4
2.3.1 虛擬資產模擬方法 .................... 7
2.3.2 幾何布朗運動參數估計模型(GBM) ....... 10
2.3.3 模擬結果 ............................ 11
3 選擇權評價分析系統 13
3.1 選擇權評價分析系統 ........................ 13
3.1.1 檔案內容 ............................ 13
3.1.2 歐式與美式選擇權評價 ................ 13
3.1.3 價格比較 ............................ 14
3.1.4 說明 ................................ 14
3.2 虛擬資產模擬分析系統 ...................... 15
3.2.1 模型 ................................ 15
3.3 模型參數估計系統 .......................... 15
3.3.1 模型與方法 .......................... 15
4 系統操作介紹 16
4.1 啟動選擇權評價分析系統 .................... 16
4.2 選擇權評價分析操作說明 .................... 16
4.3 虛擬資產模擬分析操作說明 .................. 17
4.4 模型參數估計操作說明 ...................... 17
4.5 匯入資料操作說明 .......................... 17
4.6 舉例說明 .................................. 18
5 資料分析 19
5.1 資料來源 .................................. 19
5.2 實證結果 .................................. 19
6 結論 20
附錄 34

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