政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/35758

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/35758

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政大典藏 > College of Social Science > Department of Economics > Theses > Item 140.119/35758

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/35758

Title:	準蒙地卡羅法於多資產路徑相依債券之評價
Authors:	張極鑫 Chang, Chi-Shin
Contributors:	廖四郎張極鑫 Chang, Chi-Shin
Keywords:	結構型商品多資產路徑相依商品變異數縮減法準蒙地卡羅模擬法布朗橋結構主成份分析法 Structured Products Multi-asset and Path-dependency Products Variance Reduction Techniques Quasi-Monte Carlo simulation Brownian Bridge Construction Principal Component Analysis
Date:	2005
Issue Date:	2009-09-18 15:56:59 (UTC+8)
Abstract:	近年來隨著法規與市場逐漸的開放，使得券商可以發行衍生性商品的種類也逐漸增加，而在眾多結構型商品中，不少商品其連結標的包含了多資產與路徑相依條款，可以看成投資一藍子股票且具有多個觀察時間的商品，一方面若連結資產上漲投資人將可得到一定的報酬，另外一方面同時具有下方保護的條款可避免本金嚴重虧損。而此類商品包含了多資產連結且有路徑相依條款，在評價方面是一個高維度的問題，若使用傳統的蒙地卡羅法來評價，因其收斂速度緩慢常需秏費大量的計算時間，使得蒙地卡羅法在應用上有此缺點，一般來說可以使用對立變數法或控制變數法來改進收斂的速度，另外也可以使用低差異性數列即所謂的準蒙地卡羅法來改進收斂速度，並且準蒙地卡羅法與布朗橋結構或主成份分析法相結合還可加快收斂速度。本文主要提供二種不同報酬型態的商品，第一個商品為低維度上入局商品，其報酬型態與障礙型選擇類似，第二個商品為連結多資產且路徑相依商品，以此兩商品來探討各種不同方法在不同報酬型態下的收斂速度與準確性，最後文中模擬的結果顯示在所有方法中，使用準蒙地卡羅法結合主成份分析法皆可以得到不錯的收斂速度與準確性。
Reference:	[1] Acworth, P , Broadie, M., and Glasserman , P. (1998). A comparison of some Monte Carlo and quasi Monte Carlo methods for option pricing , pp1-18 in Monte Carlo and Quasi-Monte Carlo Methods 1996, P.Hellekalek , G.Larcher , H.Niederreiter , and P.Zinterhof , eds., Springer-Verlag, Berlin. [2] Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. New York: Springer. [3] Jäckel, P. 2002. Monte Carlo Methods in Finance. New York: John Wiley & Sons. [4] Junichi Imai and Ken Seng Tan(2002).Enhanced Quasi-Monte Carlo Methods with Dimension Reduction. [5] Lemieux,C. , and Cieslak, M. , and Luttmer, K. (2002) .RandQMC user’s guide a package for randomized quasi-Monte Carlo methods in C , Technical Report 2002-712-15, Department of Computer Science , University of Calgary , Calgary , Canada. [6] Paolo Brandimarte(2002).Numerical Methods in Finance. Wiley Inter-Science [7] Pierre L"Ecuyer(2004).Quasi-Monte Carlo Methods in Finance [8] Xiaoqun Wand and Kai-Tai Fang(2002).The effective dimension and quasi-Monte Carlo integration. [9] Xiaoqun Wang and Ian H.Sloan(2006). Brownian Bridge and Principal Component Analysis:Towards Removing the Curse of Dimensionality.
Description:	碩士國立政治大學經濟研究所 93258013 94
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0093258013
Data Type:	thesis
Appears in Collections:	[Department of Economics] Theses

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