隨機化準蒙地卡羅模擬法在資產風險值估計上之探討

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Title:	隨機化準蒙地卡羅模擬法在資產風險值估計上之探討
Other Titles:	Randomized quasi-Monte Carlo efficiency in portfolio value-at-risk estimation methods
Authors:	王璇潔;Wang, Hsuan-chieh
Contributors:	淡江大學統計學系碩士班林志娟;Lin, Jyh-jiuan
Keywords:	資產風險值;蒙地卡羅;隨機化準蒙地卡羅;相對綜合指標;回溯測試;Portfolio Value-at-Risk;Randomized Quasi Monte Carlo;Monte Carlo;simulation;Back-testing
Date:	2010
Issue Date:	2010-09-23 16:42:49 (UTC+8)
Abstract:	本研究主要為探討資產風險值的估計方法。在許多風險值的估計方法中的全方位評價方法較局部評價方法來的較精確，但全方位評價方法(例如蒙地卡羅模擬法)，可能係因為大量式密集運算較為耗時的缺點，因此並未被大量採用。蒙地卡羅模擬法的優勢除了精確之外，還能處理非線性資產報酬的評價。然而隨機化準蒙地卡羅模擬法透過低差異性數列在某些條件下，可以改善蒙地卡羅模擬法耗時的缺失。因此本研究採用隨機化準蒙地卡羅法並且透過兩種較常見的低差異性數列-Halton數列及Sobol數列，同時搭配資產厚尾特性的一般化誤差分配(generalized error distribution, GED)及考慮多項資產價格相關性之Chloesky分解法進行隨機化準蒙地卡羅模擬法來估計投資組合風險值。為了能進行各種風險值估計方法的比較，本研究會同時採用下列八種方法：歷史模擬法、變異數─共變異數法、GED蒙地卡羅模擬法、Cholesky蒙地卡羅模擬法以及分別搭配Halton與Sobol數列的GED和Cholesky的隨機化準蒙地卡羅模擬法，來建構資產報酬率的風險值，並且利用回溯測試和資金運用的效率性來評估風險值各估計方法的優劣，最後，使用實際的資料做一實證分析。實證分析的結果顯示，隨機化準蒙地卡羅模擬法考慮資產厚尾特性下使用Sobol低差異性數列的模型在計算時間相對效率以及相對綜合指標分析中的表現較優於其他模型。 The portfolio Value-at-Risk estimation methods will be discussed in this research. Value-at-Risk estimation methods are classified into full evaluation methods and local evaluation methods by Jorion(2001). Monte Carlo simulation method is one of the full evaluation methods which usually used for handling nonlinear portfolios. Though it’s more accurate in estimation, however, Monte Carlo simulation method suffers from some drawbacks. One of the drawbacks is its heavily time consumption due to its intensive computational requirement. To enhance the standard Monte Carlo methods, variance reduction techniques are usually adopted. There are many commonly used alternatives: control variates, importance sampling, stratified sampling, and quasi-Monte Carlo simulation. In this research we use randomized quasi- Monte Carlo simulation methods incorporated the two commonly used low discrepancy sequences-Halton and Sobol sequences for the portfolio Value-at-Risk estimation problem. To show its efficiency, other methods will be also conducted and compared. To be more precise, we will exam the following eight Value-at-Risk estimation methods: historical simulation methods, variance-covariance metrics method, GED Monte Carlo simulation method, Cholesky Monte Carlo simulation method, GED randomized quasi-Monte Carlo simulation method, Cholesky randomized quasi-Monte Carlo simulation method. Among the quasi-Monte Carlo methods, Halton and Sobol sequencies are adopted respectively. Back-testing, mean square error and the Capital Efficiency will be used to assess the performance of those estimation methods. Besides, a new aggregate relative index is proposed. An empirical example will also be provided in this research. The empirical results show that, under the consideration of heavy-tailed, Randomized Quasi-Monte Carlo Simulation Method incorporates Sobol sequence outperforms the rest of the 7 estimation methods in terms of the aggregate relative index.
Appears in Collections:	[Graduate Institute & Department of Statistics] Thesis

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