Spectral分解法在風險值之應用:台灣市場實証

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姓名

賴映竹(Ying-chu Lai) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

Spectral分解法在風險值之應用:台灣市場實証
(Applying Spectral Decomposition in Value-at-Risk: Empirical Evidence of Taiwan Stock Market)

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摘要(中)

隨著時代的變遷與進步，越來越多的金融商品的創新，供公投資大眾或法人更多的選擇去做投資或避險，也因此使得財務槓桿上的風險越來越受到重視；不論新舊巴塞爾協定，均對金融業的投資風險、流動性風險、信用風險…等，多加規範，風險值的計算也日趨廣泛應用，蒙地卡羅模擬即為其中常用的衡量方法，而其中最重要的步驟就是分解相關係數矩陣；目前最常使用的是Cholesky分解法，然而，Cholesky分解法仍對被分解的相關係數矩陣多所限制，僅能分解正定矩陣，為了克服這個問題，我們可以採用Spectral分解法來替代Cholesky分解法，本篇論文即在探討Spectral分解法在風險值的應用，欲證明Spectral分解法能解決Cholesky分解法上的限制問題，應為計算風險值時的較佳選擇。

摘要(英)

Since more and more financial products have been invented, we have more ways to get more variety payoff and hedging. As a result, how to control financial risk becomes more and more important. Monte Carlo Simulation is the most widely used method to conduct value-at-risk. The most important part of computing value-at-risk of an asset portfolio is to derive the default correlation matrix to apply into Monte Carlo Simulation. Generally, we use the Cholesky decomposition to decompose the correlation matrix. However, there are some limitations to the Cholesky decomposition. The Cholesky decomposition cannot be used to decompose a non-positive correlation matrix. Under this circumstance, we may adopt the Spectral decomposition. This paper will show the efficiency of Spectral decomposition when facing the non-positive correlation matrix. Due to having fewer limitations, the Spectral decomposition could be more widely used rather than the Cholesky decomposition.

關鍵字(中)

★ 蒙地卡羅模擬
★ 風險值
★ Spectral分解法
★ Cholesky分解法

關鍵字(英)

★ Spectral decomposition
★ Monte Carlo
★ VaR
★ Cholesky

論文目次

I. Introduction: 1
1-1 Motivation: 1
1-2 Purpose: 2
1-3 Reference Review: 3
II. Methodology: 6
2-1 Data: 6
2-2 Decomposition methodology: 9
2-2-1 Spectral decomposition: 9
2-3 VaR evaluation methods: 10
2-3-1 Equally Weighted Moving Average approach: 11
2-3-2 Exponential Weighted Moving Average approach: 12
2-3-3 Monte Carlo Simulation: 13
2-3-4 History Simulation Approach: 14
2-4 VaR Tests: 15
2-4-1 Likelihood Ratio Test (LR Test): 15
2-4-2 Z test: 15
2-4-3 Uncovered Quadratic Value(UQV): 16
III. Applications to Equity Portfolio: 16
3-1 Statistics of Data: 16
3-2 Positive default correlation case—Cholesky decomposition & Spectral decomposition: 19
3-3 Non-positive default correlation case—Spectral decomposition: 21
IV. Conclusion: 25
Reference: 27

參考文獻

B.H. Boyer, M.S. Gibson, and M. Loretan, 1997, “Pitfalls in tests for changes in correlation,” International Finance Discussion paper #597
C.O. Alexander and C.T. Leigh, 1997, “On the Covariance of Matrices used in Value-at-Risk Models,” Journal of Derivatives
Chuang-Chang Chang, Shu-Ying Lin and Chi-Lun Lu, 2006, “Using the Spectral Decomposition Method to Price CDOs,” National Central University
D.R. Cox, 1961, “Prediction by Exponentially Weighted Moving Averages and Related Methods,” Journal of the Royal Statistical Society: Series B(Methodological), Vol. 23, No.2, pp. 414-422
Darryll Hendricks, 1996, “Evaluation of Value-at-Risk Models Using Historical Data,” FRBNY Economic Policy Review
Eugene F. Fama and Kenneth R. French, 1992, “Common risk factors in the returns on stocks and bonds,” Journal of Financial Economics, Vol.33, pp. 3-56
J.P. Morgan & Reuters, 1996, “RiskMetrics Technical Document 4th edition”
Jorion, Phillipped, 1997, “Value at Risk 2nd edition,” McGraw-Hill International Edition
K. Tanabe and M. Sagae, 1992, “An Exact Cholesky Decomposition and the Generalized Inverse of the Variance-Covariance Matrix of Multinomial Distribution, with Applications,” Journal of the Royal Statistical Society: Series B(Methodological), Vol. 54, No.1, pp. 211-219
Matthew Pritsker, 1996, “Evaluating Value-at-Risk Methodologies: Accuracy versus Computational Time,” Working Paper Series
R.F. Engle and S. Manganelli, 1999, “CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,” Journal of Business and Economic Statistics, 22, 367-381
R.F. Engle and S. Manganelli, 2001, “Value at Risk in Finance,” Working Paper Series,
Riccardo Rebonato, Peter Jackel, and Quantitative Research Centre of the NatWest Group, 1999, “The most general methodology to create a valid correlation matrix for risk management and option pricing purposes”

指導教授

林淑瑛、張傳章
(Shu-ying Lin、Chuang-chang Chang)

審核日期

2007-7-17

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