跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 許致榕
Chih-Jung Hsu
論文名稱： Importance sampling for VaR and ES calculations under GARCH model
指導教授： 傅承德
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 35
中文關鍵詞： 風險價值 、條件風險值 、厚尾 、GARCH模型
外文關鍵詞： Value-at-risk, Expected shortfall, Heavy tailed, GARCH model
相關次數： 點閱：14  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 風險價值（VaR）不只廣泛應用在投資組合的風險測量上，也成為風險管理的重要基準；條件風險值（ES）也是風險測度指標而且包含更多關於分布尾端的資訊。因此，VaR和ES的評估精確度受到越來越多的關注。在此篇論文，我們使用一個對稱的GARCH（1,1）模型。然後，我們採用一個方法－importance sampling technique，來減少變異數且精確地估計VaR與ES。此外，importance sampling technique可以得到與其他的方法一樣的精確度但卻使用較少的樣本。在最後，我們展示我們的方法importance sampling technique優於其他方法。

    Value-at-risk (VaR) is not only broadly used in portfolio risk measurement but also becomes an important benchmark in risk-management. Moreover, expected shortfall (ES) is a risk measure and has more information about the distribution of returns in the tail. Thus, evaluating precision of VaR and ES is getting more attention. In this paper, we suggest a symmetric GARCH(1,1) model to fit the loss data. Then, we propose an importance sampling technique to reduce the variance and estimate VaR and ES accurately. Besides, we find the method with importance sampling which can get the same precision like other methods but using less sample sizes. In the end, we show the method with importance sampling technique outperforms other methods.

    Contents 摘要 i Abstract ii 致謝 iii List of Figures vi List of Tables vii 1 Introduction 1 2 Preliminaries 3 2.1 Model 3 2.2 Risk measure 4 3 Estimation methods 6 3.1 Historical simulation 6 3.2 Normal and T conditional distribution 7 3.3 The Hill estimator 8 3.4 Filtered historical simulation 9 3.5 Importance sampling 10 3.3.2 The normal distribution case 10 3.3.2 The t-distribution case 15 4 Numerical results 22 4.1 The normal case 22 4.2 The t-distribution case 24 4.3 Empirical Study 29 5 Conclusion 31 Reference 33

    Andreev, A. and A. Kanto (2005). Value-at-risk prediction: A comparison of alternative strategies. Journal of Risk 7 (2), 55-61.
    Baillie, R. and T. Bollerslev (1989). The message in daily exchange rates: A conditional variance tale. Journal of Business and Economic Statistics 7, 297-309.
    Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-27.
    Bollerslev, T. (1987). A conditionally heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69, 542-547.
    Cheng-Der Fuh, Inchi Hu, Y.-H. H. and R.-H. Wang (2010). Efficient simulation of value at risk with heavy-tailed risk factors. Operations Research 59 (6), 1395-1406.
    Chriso ersen, P. and S. Goncalves (2005). Estimation risk in financial risk management. Journal of Risk 7 (3).
    Do, K.-A. and P. Hall (1991). On importance resampling for the bootstrap. Biometrika 78 (1), 161-167.
    Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of united kingdom inflation. Econometrica 50, 987-1007.
    Fuh, C. and I. Hu (2004). Efficient importance sampling for events of moderate deviations with applications. Biometrika 91 (2), 471-490.
    Fuh, C. and I. Hu (2007). Estimation in hidden markov models via efficient importance sampling. Bernoulli 13 (2), 492-13.
    Giovanni Barone-Adesi, K. G. and L. Vosper (1999). Var without correlations for nonlinear portfolios. Journal of Futures Markets 19, 583-602.
    Hall, P. (1991). Bahadur representations for uniform resampling and importance resampling with applications to asymptotic relative eciency. Annals of Statistics 19,
    1062-1072.
    Hill, B. (1975). A simple general approach to inference about the tail of a distribution.Annals of Statistics 3, 1163-74.
    Hull, J. and A. White (1998). Incorporating volatility updating into the historical simulation method for var. Journal of Risk 1, 5-19.
    Kuester, K., S. M. and M. S. Paolella. (2006). Value-at-risk prediction: A comparison of alternative strategies. Journal of Financial Econometrics 4, 53-89.
    Mancini, L. and F. Trojani (2011). Robust value at risk prediction. Journal of Financial Econometrics, 1-33.
    McNeil, A. J. and R. Frey. (2000). Estimation of tail-related risk measures for heteroscedastic fi nancial time series: An extreme value approach. Journal of Empirical
    Finance 7, 271-300.
    Nelsen, R. B. (1999). An introduction to copulas.
    Paul Glasserman, P. H. and P. Shahabuddin (1999). Asymptotically optimal importance sampling and strati cation for pricing path-dependent options. Mathematical
    Finance 9, 117-152.
    Paul Glasserman, P. H. and P. Shahabuddin (2000). Variance reduction techniques for
    estimating value-at-risk. Management Science 46, 1349{1364.
    Paul Glasserman, P. H. and P. Shahabuddin (2002). Portfolio value-at-risk with heavy-tailed risk factors. Mathematical Finance 12(3), 239-269.
    Pritsker, M. (1997). Towards assessing the magnitude of value-at-risk errors due to errors in the correlation matrix. Financial Engineering News, 14-16.
    Shih-Kuei Lin, R.-H. W. and C.-D. Fuh (2006, September). Risk management for linear and non-linear assets: A bootstrap method with importance resampling to evaluate
    value-at-risk. Asia-Paci c Financial Markets 13, 261-295.

    QR CODE
    :::