我們在一個隨機波動率模型的共同框架下計算了體系風險指標∆CoVaR，並且利用重要性採樣技術來提高蒙特卡洛模擬的準確性。運用Spearman correlation, 將∆CoVaR 識別出的系統重要性的金融機構與其他體系風險指標識別出的排名相比較。本模型至少存在三個優勢。首先，非參數法不依賴對於分佈假設。第二，動態隨機波動率矩陣模型允許我們直接根據∆CoVaR的定義來計算。第三，它使得我們可以在統一框架下計算不同的體系風險指標。

We calculate the systemic risk measure ∆CoVaR in a framework of Dynamic Volatility Matrix Models and apply the technique of importance sampling to augment the accuracy of Monte Carlo simulation. The ranking of systemically important financial institutions (SIFIs) identified by ∆CoVaR will be compared with other systemic risk measure ranking by Spearman correlation. This modelling framework has at least three advantage over the traditional approaches. Firstly, the non-parametric method does not rely on the assumption of distribution. Second, our dynamic stochastic volatility matrix models allow estimating ∆CoVaR directly according to its definition. Third, it allows us to compute different systemic risk measure with the same method that is more suitable for the comparison of different measures.

Chapter 1 Introduction and Literature Review 1
Chapter 2. ∆CoVaR Estimation under Dynamic Volatility Matrix Models 5
2.1 Systemic risk measures 5
2.2 Dynamic Volatility Matrix Models 6
Chapter 3. Volatility Estimation: Fourier Transform Method 8
3.1 Fourier Transform Method 8
3.2 Parameter estimation for stochastic volatility/correlation model 10
3.3 Simulation studies 11
Chapter 4. Importance Sampling: Variance Reduction 17
4.1 Definition of ∆CoVaR 17
4.2 Calculation of ∆CoVaRq under two dimension Geometric Brownian Motions system 17
4.3 Numerical Examples 21
Chapter 5. Empirical Analysis 22
5.1 Data Set 22
5.2 Empirical Results 23
5.2.1 ∆CoVaR computation 23
5.2.3 Compared with other Capital Shortfall Measures 26
5.2.2 System important financial institution identification 30
Conclusion 34
REFERENCE 35
Appendix Ⅰ:Quantile regression to estimate CoVaR 36
Appendix Ⅱ: CoVaR estimation under GARCH-DCC 38
Appendix Ⅲ: SRISK Definition 40

Adrian, T., Brunnermeier, M. K. (2016). CoVaR. The American Economic Review, 106(7), 1705-1741
Acharya V V, Pedersen L H, Philippon T, et al. (2017) Measuring systemic risk [J]. The Review of Financial Studies, 30(1): 2-47.
Mancino M E, Recchioni M C, Sanfelici S. (2017) Fourier-Malliavin volatility estimation: Theory and practice [M]. Springer Briefs in Quantitative Finance: Springer.
Mainik G, Schaanning E. (2014) On dependence consistency of CoVaR and some other systemic risk measures [J]. Statistics & Risk Modeling, 31(1): 49-77.
BISIAS, Dimitrios, et al. (2012) A survey of systemic risk analytics. Annu. Rev. Financ. Econ., 4.1: 255-296.
Brownlees, C., Engle, R. F. (2016). SRISK: A conditional capital shortfall measure of systemic risk. The Review of Financial Studies, 30(1), 48-79.
Change and Han(2011).Corrections to Dynamic Volatility Matrix Estimation by Fourier Transform Method. Master thesis.
Lin and Han(2018).Asymptotically Optimal Importance Sampling for Lower Tail Probability Estimation under Matrix Valued Stochastics. Master thesis.
Engle R. (2002) Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models [J]. Journal of Business & Economic Statistics, 20(3): 339-350.
Han, C. H., Liu, W. H., & Chen, T. Y. (2014). VaR/CVaR estimation under stochastic volatility models. International Journal of Theoretical and Applied Finance, 17(02), 1450009.
Fouque, J. P., & Langsam, J. A. (Eds.). (2013). Handbook on systemic risk. Cambridge University Press.
Billio, M., et al. (2012). "Econometric measures of connectedness and systemic risk in the finance and insurance sectors." Journal of Financial Economics 104(3): 535-559.
Giglio, S., et al. (2016). "Systemic risk and the macroeconomy: An empirical evaluation." Journal of Financial Economics 119(3): 457-471.
Giglio S.(2011)Credit default swap spreads and systemic financial risk[J]. Proceedings, Federal Reserve Bank of Chicago, 2011, 10(9): 104-141.
Girardi, Giulio, and A. Tolga Ergün. (2013) "Systemic risk measurement: Multivariate GARCH estimation of CoVaR." Journal of Banking & Finance 37.8: 3169-3180.
Laeven, L., et al. (2016). "Bank size, capital, and systemic risk: Some international evidence." Journal of Banking & Finance 69: S25-S34.
Koenker, R. W. (2005). Quantile Regression, Cambridge U. Press