臺灣博碩士論文加值系統

本研究主要在探討與比較使用蒙地卡羅模擬法對路徑相依新奇選擇權訂價時，各種效率改善的技巧所能夠提供的效率與精確性的改善效果。
在效率改善方面，本研究是比較一般的蒙地卡羅模擬法與使用效率改善技巧的蒙地卡羅模擬所得的價格，在變異數上的改善程度作為效率改善的指標。而在精確度改善方面，本研究透過比較使用各種效率改善技巧，並經過收斂以後所得的模擬價格與理論價格的差異，作為精確度改善的指標。
經由上述的方法，本研究比較了不同的效率改善技巧之間在速度、效率與精確度的改善效果。同時在評價障礙選擇權與回顧選擇權時，加入條件機率的概念來降低蒙地卡羅模擬過程中的偏誤。

This paper studies how different efficiency improvement techniques can improve efficiency and accuracy when we use Monte Carlo simulation in pricing path-dependent exotic options.
In this paper, we compare the variances of simulation prices obtained by using naïve Monte Carlo simulation with those obtained by using Monte Carlo simulation with different efficiency improvement techniques. The results represent improvement in effieciency. We also compare the simulation price obtained by using Monte Carlo simulation with different efficiency improvement techniques with analytical solutions to check improvement in accuracy.
Through the approaches mentioned above, we compare improvements in speed, efficiency, and accuracy of different efficiency improvement techniques.Besides, this paper also use the concept of conditional probability to improve accuracy in pricing barrier options and lookback options

目錄
口試委員會審定書
誌謝 i
中文摘要 ii
英文摘要 iii
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究方法 2
1.3 章節概要 4
第二章 選擇權商品與一般蒙地卡羅模擬法簡介 5
2.1 標準選擇權介紹 5
2.2 包裹選擇權介紹 5
2.3 新奇選擇權介紹 18
2.4 蒙地卡羅模擬與選擇權訂價 28
第三章 文獻探討 31
3.1 對偶變數法 31
3.2 分層抽樣法 33
3.3 變數控制法 35
3.4 重要性抽樣法 37
3.5 配合動差法 37
3.6 二元樹取樣法 38
3.7 局部二元樹取樣法 39
第四章 路徑相依新奇選擇權訂價與蒙地卡羅模擬 42
4.1 標準選擇權的訂價與蒙地卡羅模擬 42
4.2 亞洲選擇權的訂價與蒙地卡羅模擬 51
4.3 障礙選擇權的訂價與蒙地卡羅模擬 61
4.4 回顧選擇權的訂價與蒙地卡羅擬 75
第五章 結論 85
參考文獻 89
附錄：二元樹取樣法標準誤上界的推導 92

參考文獻
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