應用極值理論於風險值之估計與保險業風險資本額制度之研究

投資人與主管機關對於極值報酬皆非常重視，而風險管理為降低極值報酬所帶來的衝擊的關鍵，風險值(Value at Risk, VaR)是一種評估風險的方法，風險值代表在正常的巿場情況與特定的信賴水準下，在某特定期間內所衡量出來最大的預期損失，而在不同分配與參數假設下，形成不同的風險值模型。極值理論以配適尾部分配聞名，而非將整個分配列入考慮，本研究將把極值理論應用於風險值模型，並將其與傳統的風險值模型做比較。本研究將比較五種風險值模型(SMA、EWMA、歷史模擬法、最大概似估計之極值理論與機率加權動差法估計之極值理論)，且將衡量之時間軸分為排除與未排除2008年金融海嘯兩段，並以準確度測試與保守度測試評量風險值模型之風險估計結果，評估結果顯示應用極值理論之風險值之準確度與保守度較位應用極值理論之傳統風險值模型為高。最後，我們亦將極值理論應用於計算保險業之風險基礎資本額(RBC)公式中之C-1風險的權益風險(Equity Risk)，我們以RBC公式與極值理論分別計算權益風險，結果顯示以及極值理論衡量之權益風險較RBC公式所計算出之結果為高，此結果表示以極值理論所衡量之權益風險較為保守。本研究主要提供企業與主管機關於進行風險管理時一新觀點，因為極值理論僅將區域之極端報酬列入計算，忽略分配中之其他報酬是否會導致不可靠的結果，未來有關極值理論可進行更深入的研究。

關鍵字

極值理論；風險值；風險資本額制度

並列摘要

Extreme returns are of the most concern to investors and regulators. Risk management is the key to reduce the impact of extreme returns. Value at Risk (VaR) has been used as a measure of risk. VaR estimates the largest potential loss to investors in a specified investment horizon at the specified confidence interval. Various VaR models have been developed under different assumptions. The extreme value theory (EVT) fits only the extreme values to a distribution instead of taking the whole distribution into consideration. We seek to apply the EVT to calculate the VaR and compare it to other models in this paper. We use five VaR models (SMA, EWMA, historical simulation, EVT estimated by MLE and PWM) and calculate VaR for two time horizons, one excludes the financial tsunami and the other one includes it. The measure of accuracy and the measure of conservatism are conducted for evaluation. The evaluation results indicate that with the utilization of the EVT, the VaR is more accurate and conservative than other traditional methodologies. We also apply the EVT to calculate the equity risk of C-1 risk factor in the risk-based capital (RBC) formula. The equity risk is measured by both the original RBC formula and the EVT. The results tell us that the equity risk estimated by the EVT is higher, which means that it is more conservative than the original formula. Since we take only extreme returns within each block into calculation, chances are that the ignorance of other values might unreliable results. More discussion of the EVT application to insurance can be conducted in the future. We provide a new point of view for the insurance regulators while setting regulations for insurance companies.

並列關鍵字

Extreme value theory (EVT) ； Value at Risk (VaR) ； Risk-based capital (RBC)

參考文獻

Beder, T.S. (1995) “VaR: Seductive but Dangerous.” Financial Analysis Journal, September-October, pp.12–24.

Bradley B.O. and Taqqu M.S. (2001) “ Financial Risk and Heavy Tails.” Svetlozar T. Rachev, editor, North Holland.

Chen, H., and Cummins J. D. (2008) “Longevity Risk Premium, Extreme Value Approach and Risk Cubic Pricing.” The 4th International Longevity Risk and Capital Markets Solutions Conference.

Diebold, F., T. Schuermann, and J. Stroughair. (1999) “Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management.” Advancesn Computational Finance, Kluwer Academic Publisers, Amsterdam.

Duffie, D., Pan, J. (1997) “An Overview of Value at Risk.” J. Derivatives 4(3), pp.7–49.

國際替代計量

應用極值理論於風險值之估計與保險業風險資本額制度之研究

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