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| Title: | 異質性投資組合下的改良式重點取樣法
Modified Importance Sampling for Heterogeneous Portfolio |
| Authors: | 許文銘 |
| Contributors: | 劉惠美
許文銘 |
| Keywords: | 投資組合
信用風險
尾端機率
蒙地卡羅法
重點取樣法
改良式重點取樣法
變異數縮減
Portfolio credit risk
Tail probability
Monte Carlo
Importance sampling
Modified importance sampling
Variance reduction |
| Date: | 2016 |
| Issue Date: | 2016-07-01 14:57:13 (UTC+8) |
| Abstract: | 衡量投資組合的稀有事件時，即使稀有事件違約的機率極低，但是卻隱含著高額資產違約時所帶來的重大損失，所以我們必須要精準地評估稀有事件的信用風險。本研究係在估計信用損失分配的尾端機率，模擬的模型包含同質模型與異質模型；然而蒙地卡羅法雖然在風險管理的計算上相當實用，但是估計機率極小的尾端機率時模擬不夠穩定，因此為增進模擬的效率，我們利用Glasserman and Li (Management Science, 51(11),2005)提出的重點取樣法，以及根據Chiang et al. (Joural of Derivatives, 15(2),2007)重點取樣法為基礎做延伸的改良式重點取樣法，兩種方法來對不同的投資組合做模擬，更是將改良式重點取樣法推廣至異質模型做討論，本文亦透過變異數縮減效果來衡量兩種方法的模擬效率。數值結果顯示，比起傳統的蒙地卡羅法，此兩種方法皆能達到變異數縮減，其中在同質模型下的改良式重點取樣法有很好的表現，模擬時間相當省時，而異質模型下的重點取樣法也具有良好的估計效率及模擬的穩定性。
When measuring portfolio credit risk of rare-event, even though its default probabilities are low, it causes significant losses resulting from a large number of default. Therefore, we have to measure portfolio credit risk of rare-event accurately. In particular, our goal is estimating the tail of loss distribution. Models we simulate are including homogeneous models and heterogeneous models. However, Monte Carlo simulation is useful and widely used computational tool in risk management, but it is unstable especially estimating small tail probabilities. Hence, in order to improve the efficiency of simulation, we use importance sampling proposed by Glasserman and Li (Management Science, 51(11),2005) and modified importance sampling based on importance sampling which proposed by Chiang et al. (2007 Joural of Derivatives, 15(2),). Simulate different portfolios by these two of simulations. On top of that, we extend and discuss the modified importance sampling simulation to heterogeneous model. In this article, we measure efficiency of two simulations by variance reduction. Numerical results show that proposed methods are better than Monte Carlo and achieve variance reduction. In homogeneous model, modified importance sampling has excellent efficiency of estimating and saves time. In heterogeneous model, importance sampling also has great efficiency of estimating and stability. |
| Reference: | 1. Bassamboo, A.,Juneja, S.and Zeevi, A. (2008) , “Portfolio Credit Risk with 2. Extremal Dependence: Asymptotic Analysis and Efficient Simulation” , Operations Research, 56(3), 593-606
2. Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007), “An Efficient Algorithm for Basket Default Swap Valuation”, Joural of Derivatives, 15(2), 8-19
3. Fuh, C.D., Teng, H.W., and Wang, R.H. (2013), “Efficient Importance Sampling for Rare Event Simulation with Applications”, Technical Report.
4. Glasserman, P. (2004), “Tail Approximations for Portfolio Credit Risk”, Journal of Derivatives, 12, 24-42
5. Glasserman, P. and Li, J. (2005), “Importance Sampling for Portfolio Credit Risk”, Management Science, 51(11), 1643-1656
6. Han,C.H. ,Wu,C.T. (2010), “Efficient Importance Sampling for Estimating Lower Tail Probabilities under Gaussian and Student’s t Distributions”, Preprint. National Tsing-Hua University. 2010
7. Li, D.X. (2000), “On Default Correlation: A Coupla Function Approach”, Journal of Fixed Income, 9, 43-54
8. Nocedal, J. and M. Wright (1999), “Numerical Optimization”. New York: Springer-Verlag |
| Description: | 碩士
國立政治大學
統計學系
103354010 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1033540101 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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| 010101.pdf | 2197Kb | Adobe PDF2 | 46 | View/Open |
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