臺灣博碩士論文加值系統

本論文將基於邊際和聯合機率進行 CoVaR 的模擬。此外，將提出重要抽樣法的最佳參數與分位數之間的二次模式，這可以幫助我們更有效率地找到所要估計的分位數。

In this thesis, a simulation of CoVaR based on the marginal and the joint probability would be presented. Also, a quadratic pattern between the optimal parameters of importance sampling and the quantiles will be proposed, which may help us to find the quantiles of interest more efficiently.

口試委員審定書i
致謝ii
摘要iii
Abstract iv
1 Introduction 1
2 Preliminaries 4
2.1 VaR and CoVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Importance Sampling and Exponential Tilting . . . . . . . . . . . . 6
2.3 Delta-Gamma Approximation . . . . . . . . . . . . . . . . . . . . . 8
3 Simulation under Normal Distribution 11
3.1 Model Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Alternative Distribution . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Simulation under t-Distribution 20
4.1 Model Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Alternative Distribution . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Numerical Results 29
6 Conclusion Remarks and Further Research 40

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