本文基於Acharya et al (2012)提出的systemic risk的理論下，提出用Malliavin and Mancino (2009) 提出的傅立葉轉換的方法建構動態連續時間模型來衡量體系風險。我們旨在為金融公司提供一個體系風險指標，同時，我們在不同方面來評估指標的效用。
我們分別衡量了美國、台灣及中國大陸金融公司的體系風險，以證明我們的SRISK指標對金融體系風險具有一定解釋力與預測力。監管機構可以參考這一指標來監控本國金融市場的體系風險以及個體金融機構對整體風險的貢獻。

In this paper, we follow the framework of measuring systemic risk proposed by Acharya et al (2012). We use the non-parametric Fourier transform method proposed by Malliavin and Mancino (2009) to construct the dynamic continuous-time model which aims to estimate the form of capital shortfall to provide a systemic risk indicator for financial firms. At the same time，we evaluate this indicator in several aspects.
We measure the systemic risk (SRISK) of financial firms in the United States, Taiwan and China to verify that the indicator has a certain ability to explain and predict financial system risk. Regulators can access this indicator to catch the whole systemic risk of domestic financial markets and the contribution of the individual enterprise to the system risk.

1.Background and Literature Review 6
1.1 What We Need to Know First about Systemic Risk 7
1.2 Literature Review 7
2. Systemic Risk Measures 10
2.1 Conditional Capital Shortfall 10
2.2 Long Run Marginal Expected Shortfall 11
3 Parameter estimation for dynamic volatility matrix model 12
3.1 Dynamic Processes of Stochastic Volatility and Stochastic Correlation 12
3.2 Instantaneous Volatility Matrix Estimation by Non-parametric Fourier Transform Method 13
3.2 Parameter Estimation via MLE 15
3.4 Simulation Study 16
4 Data and SRISK Measurement 17
4.1 SRISK Measurement 18
4.2 Compared with Other Capital Shortfall Measures 18
5 Empirical Studies on SRISK 20
5.1 SRISK’s Evolution and Ranking in USA 20
5.2 SRISK in Prediction of Trouble Relief 21
5.3 Macroeconomic Condition’s Prediction with SRISK 22
5. 4 Robustness Test 23
6 SRISK in Other Regions 24
6. 1 SRISK in Taiwan and China 24
6. 2 Driving Factors of SRISK 25
6. 3 Can SRISK Help Investment？ 26
7 Conclusion & Future Research 28
Reference 29
Table & Figure 32
Table 1: Parameters Setting 32
Table 2: Classification for Sample in US 32
Table 3: Heston-Jacobi Parameter Estimation by Firms 33
Table 4：Heston-Jacobi Parameter Estimation by Time 33
Table 5: SRISK% Ranking 34
Table 6：TARP Capital Injection 35
Table 7: Macroeconomic Predictive Regression 36
Table 8: Macroeconomic Predictive Regression 37
Table 9: SRISK Ranking Correlation 37
Table 10: Classification for Sample in Taiwan 38
Table 11: Classification for Sample in China 39
Figure 1: Simulation of Market Index & Firm’s Volatility 40
Figure 2: Simulation of Market Index & Firm’s Correlation 40
Figure 3: Time Series Changes of All Company Average Heston Parameters 41
Figure 4: Aggregate SRISK by Sector in US 41
Figure 5： SRISK of Goldman Schas, Citi and Leman Brothers 42
Figure 6：Aggregate SRISK by Sector in Taiwan and China 42
Figure 7：Leverage in SRISK 43
Figure 8：HHI of SRISK 44
Figure 9：Performance of Strategy Based on SRISK 45

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