## 研究報告

 標題 GARCH 模型下之風險值效率模擬與近似計算 100 1 2011/08/01 GARCH 模型下之風險值效率模擬與近似計算 Efficient Simulation and Approximation of Value at Risk under Garch Model 王仁和 淡江大學財務金融學系 計畫編號：NSC100-2410-H032-024 研究期間：20110801~20120731 研究經費：260,000 行政院國家科學委員會 In this research plan, we consider using flexible and elastic Monte Carlo simulation to evaluate the Value-at-Risk under the GARCH model, then use importance sampling to reduce the high computational cost problem of Monte Carlo simulation method. Apply the latest moderate deviation method to calculate the optima efficiency of the importance sampling method, and improve the computational efficiency of Monte Carlo simulation. Empirically, we can collect some prices on domestic and foreign stocks or indexes from Datastream and TEJ databases. Use the ARCH-LM test (Lagrange Multiplier Test) and the Ljung-Box Q2 statistics to test whether the data are heteroskedastic. Then, estimate the unknown parameters of the GARCH model. Finally, run the Monte Carlo simulation program to evaluate the Value-at-Risk and do back-testing to check the efficiency of model.;本研究考慮在GARCH 模型下，採用靈活且彈性高的蒙地卡羅模擬法計算風險值， 並探討利用重點抽樣法降低蒙地卡羅模擬法的計算成本高的問題。採用最新的中偏差 法計算出最佳效率的重點抽樣法，提高蒙地卡羅模擬法的計算效率。 實證方面，從Datastream 及台灣經濟新報資料庫蒐集一些國內外股票或指數的資 料，用ARCH-LM 檢定 (Lagrange Multiplier Test) 及 Ljung-Box Q2 統計量檢定資 料是否有異質變異，檢定後再進行GARCH 模型的參數估計。最後用蒙地卡羅模擬法程 式來估算風險值並進行回溯測試。 重點抽樣法; 蒙地卡羅模擬法; 風險值; 回溯測試; Importance sampling; Monte Carlo simulation; Value-at-Risk; Back-testing 中文