指導教授：韓傳祥臺灣大學：數學研究所秦唯植Qin, Wei-ZhiWei-ZhiQin2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264030在這篇文章，我們討論了控制變異法結合重要抽樣法在亞式選擇權定價下之應用，我們以 [7] 為基礎，提出數個更動重要抽樣法準則的估計方法。並提出一些理論架構，接下來，我們討論更動控制變異的一般方法。最後，我們討論此種方法在違約機率上的計算，以及上述方法的數值結果及討論。We dicuss the Asian option pricing problem under the geometric Brown-ian motion assumption. Digec and Horrman [7] give a method based on the combination of conditional importance sampling and control variate method. First we revise the conditional important sampling part by using different im-portance sampling critique including efficient estimator and using some ap-proximation distribution. We give some theoretical support to our method. And then we give the numerical results of this revised method. Second we discuss the possibility of the control variate part to form a general method to deal with this problem. Finally we estimate the probability P (⣵76; ≥ ⣵77;) and discuss the numerical result.委員審定書 i Abstract ii 中文摘要iii Contents iv 1 Introduction 1 2 Preliminaries 4 2.1 Asian option pricing and naive simulation under Black-Sholes environment 4 2.2 Control variates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 The classical control variates for Asian option . . . . . . . . . . . 5 2.2.2 The new control variates for Asian option . . . . . . . . . . . . . 7 2.2.3 The additional control variate method . . . . . . . . . . . . . . . 8 2.3 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Different Criterion of importance sampling . . . . . . . . . . . . 11 2.3.2 Cross entropy method . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Approximation of sum of lognormal random variable . . . . . . . . . . . 14 3 Method formation 15 3.1 Review of Digence and Hormann’s Method . . . . . . . . . . . . . . . . 15 3.2 Efficient I.S approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Variance minimum I.S approach . . . . . . . . . . . . . . . . . . . . . . 19 3.4 General conditional method . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 The probability of {A C} 25 5 numerical results 27 5.1 Revised Importance Sampling results . . . . . . . . . . . . . . . . . . . 27 5.2 Default Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Conclusion 35 7.Bibliography..................362112979 bytesapplication/pdf論文公開時間：2019/08/25論文使用權限：同意有償授權(權利金給回饋本人)控制變異亞式選擇權重要抽樣法thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264030/1/ntu-103-R01221015-1.pdf