主要保險先進國家或地區對防範壽險業失卻清償能力的規範，都朝向採行資本適足性的風險基礎資本（RBC）的建制，我國亦正朝向此方向發展，而台灣財政部保險革新小組，參考的是美國「風險基礎資本制度，簡稱為RBC」，1999年保險司曾公開表示，在法令修正通過兩年後將實施RBC制度。基本上，壽險業資本適足性的建制採行RBC較單一資本制度（最低資本制度）為優，但是在RBC的設計上，除了單純的假設C1與C2風險是完全隨機發生之外，對各類的風險項目的風險係數並無適當的考量，再者對於各風險項目下的各分類項目間的相關性（或共變異性）亦無適切的考量，使本制度有其先天設計上的不完美。在台灣隨著國際化的腳步加劇，一方面國內保險公司的競爭的情形越加白熱化，且對於保險公司的規範逐漸鬆綁，因此，對壽險公司而言，面對投資商品的越趨多樣化，如何妥善的管理投資組合的市場風險是非常重要的。因此，如何訂定適合符合本國環境的RBC制度亦為當務之急，故促發本文的研究動機。 在各種管理市場風險的方法中，風險涉險值（Value at Risk）之風險衡量方法可以用來衡量整體投資組合的風險，近年來已有許多國外的銀行與監理機關採用風險涉險值來管理企業所面臨的風險。本研究依據四種不同的情境假設，運用VaR來衡量RBC制度下C1及C2的風險可能性，分別為情境一：C1及C2之相關係數為零下之風險值、情境二：實際投資組合之風險值、情境三C1及C2各風險項目以風險係數衡量下之風險值及情境四季報酬率下之風險值，再帶入RBC公式求得RBC Ratio，並利用統計之差異性檢定方法，檢定其結果後予以分析。 本研究的檢定結果顯示，情境一與二有顯著的差異，直觀的假設C1及C2為零的結果並非合理，而且從情境一樣本之RBC Ratio平均值大於情境二來看，其相關係數可能較零為大，因此我們若直觀的把其相關係數視為零的結果，有可能導致風險的低估。再者，情境二與三有顯著的差異，無法支持個別風險項目以其本身的風險係數衡量的風險結果是無異於以實際投資組合的計算方法，而且從情境二樣本之RBC Ratio平均值大於情境三來看，顯示個別計算的結果可能造成風險的高估。最後，情境二與四亦有顯著的差異，而且從情境二樣本之RBC Ratio平均值大於情境四來看，短期（季報酬率）的風險波動可能比長期（年報酬率）來的高。因此，本研究建議，未來監理機關在制定RBC制度時，應以VaR實際投資組合的方法來衡量其風險，並對於在監控邊緣的公司短期內需加以追蹤，此結果可以提供壽險業者及監理機關參考。 / In major countries and areas with highly advanced life insurance industry, the establishment of risk based capital（RBC）founded upon capital adequacy is adopted as the norm to avoid losing solvency. Basically, to adopt RBC is more superior than to adopt Minimum Capitalization System in the establishment of life insurance industry’s capital adequacy. However, except simply assuming that the risk of C1 and C2 arises completely randomly, proper consideration is given neither to the risk factor of risk items in each category, nor to the risk items’ correlation（or covariance）with the result of inherent flaw in the design of RBC. Hence, how to institute the RBC system pertinently correspondent with the circumstances in Taiwan becomes utterly imperative, and it also motivates this study to be proceeded. The risk measurement of “Value at risk” is able to be adopted to evaluate the risk of the whole portfolios. In the light of four different scenarios hypothesized in this study, VaR is in use to estimate the possibility of risk. Respectively, the four scenarios are：scenario 1：the VaR when the correlation of C1 and C2 is zero; scenario 2：the VaR of the actual portfolio; scenario 3：the VaR of each risk item of C1 and C2 measured by risk factor scenario 4：the VaR of quarterly return rate. The RBC ratio, calculated by introducing the VaR of the four scenarios into the RBC formula, is tested by the statistical differentiation test and then the result of the test is then analyzed. The result of this study manifests three observations. Firstly, there is significant difference existing between scenario 1 and 2. It is not rational to intuitively suppose that the correlation of C1 and C2 is zero. Accordingly, risk underestimation is probably induced by the result of the intuition of rating the correlation of C1 and C2 as zero. Secondly, there is significant diversity existing between scenario 2 and 3 as well. The significant discrepancy between scenario 2 and 3 can not testify that the result derived from individual risk items and their risk factors is identical with the one derived from actual portfolio. Furthermore, it is shown that risk overestimation potentially results from the consequences of respective calculation. At last, there is also outstanding difference occurring between scenario 2 and 4. In addition, the value of short-term risk likely fluctuates more intensely than long-term. To conclude, in the future it is suggested that the corresponding authorities should adopt the method via which the risk is measured in the light of actual portfolio in the attempt to establish RBC system. Meanwhile, in the short term, it is necessary to continuously supervise the operation of firms, whose unsteadily fluctuated short-term business indicators reveal potential risks. The life insurance firms and the corresponding authorities can refer the conclusions of this study mentioned above.

VaR和RBC的差別主要在於風險相關性的結構，RBC以人為的方式設定風險之間為完全相關或完全無關，而VaR則經由歷史資料估計得到相關性的結構，當然也可能因估計的誤差而造成錯誤。 本篇文章的目的為探討相關係數矩陣對於資本需求的設定是否會造成影響，我們將利用產物保險業的資料來作模擬分析，並觀察資本需求制度因為相關性結構的設定是否會影響其效率及有效性。 我們將建立一個模擬中的世界，在這個世界中，產險公司將面臨股票投資風險、利率風險和核保風險等三種風險並根據1999年底美國產險公司的平均值來設定一個起始的保險公司的財務分配狀況，經過模擬後，利用兩種比較標準來比較類似RBC和類似VaR的資本需求，第一種標準為在監理上要求某種程度的型一誤差下所造成的型二誤差，第二種為資本需求的有效性，是否能在面臨相同的破產風險下，要求較低的資本。 我們的結果可以看到因資料點的增加，使得估計誤差減少，但VaR卻未因此而此RBC來得好，經過對股票的市場價值、債券的市場價值和負債三個部位作簡單的分析發現VaR和RBC兩者問的關係約為一個近似於1的比例，而此比例會因假設的相關係數矩陣而改變。因此，當監理機關在選擇監理的制度時，是否估計相關係數矩陣並不會有太大的影響，因為對於相關性作不同假設約兩種制度之間為一個近似於1的比例。 / The major difference between risk-based capital (RBC) and value at risk (VaR) is the specification of the correlation structure among risks. RBC subjectively specifies that risks of insurers are either independent of each other or perfectly and positively correlated. Although VaR attempts to capture the underlying correlation structure through estimation of historical data, it is subject to estimation errors. The purpose of this paper is to examine how the mis-specification or mis-estimation of correlation structure affects the effectiveness of capital requirements in the property-casualty insurance industry. We first construct a representative insurer in a simulated world with stock market risk, interest rate risk, and underwriting risk. RBC-type and VaR-type of capital requirements are then calculated as the financial status of the insurer evolves. All parameters in the simulation are based on historical data to approximate the real world. We then examine the effectiveness of these two capital requirements in terms of their early warning capabilities and the levels of capital needed for various solvency rates. Our results show that the correlation estimation when using annual data has too big errors to bejustified. The capital requirement incorporating estimated correlation matrix was dominated by the one lacking correlation estimation. RBC-type requirement has lower chances to signal false alarms given the desired early warning capabilities and demands less capital for the same solvent probabilities. Insurance regulators therefore should not embrace correlation estimation into capital requirements before they could have insurance companies reported data more frequently.

所謂VaR是指，投資組合未避險部位在某一信賴水準下持有某一段時間後所可能產生的最大損失值。其基本公式為VaR=-(ut-zqt)。其中u為報酬均值 ，Z為標準常態分配累積機率值，q為報酬標準差。VaR值對投資者有兩種意義：一是瞭解部位風險，如果這個值超過本身所可以承受的範圍，應該調整投資組合或做適當的避險動作。另一點是將VaR值視為本身所可以承受的最大損失，因此應提列等額的損失準備，風險控管人員隨時監視持有部位的市場價值，當實際損失超過VaR值時，應要求立即停損出場，否則像英商霸菱銀行倒閉事件會不斷的發生。 本研究共使用的三種估算VaR的方法：歷史價格模擬法、等權移動平均法、加權移動平均法及兩種預測報酬波動度的方法：GARCH、EGARCH。以臺灣加權股價指數9、23、46、144、288天的報酬及報酬標準差為樣本，分別求算每日在信賴水準為95%、99%，持有期間為一日的VaR值，將所求得的VaR值，與隔日實際的損益相比，以隔日實際損失是否小於VaR值為效率衡量的標準，檢驗各種計算VaR方法應用在臺股指數期貨的效率之依據。 在三種估算VaR的方法中，信賴水準95%下，以使用46天等權移動平均所求算的VaR值效率最好（誤差3.25%），使用歷史價格模擬法，持有期間為九日的VaR效率最差（誤差31.25%）。信賴水準為99%時，以使用144天等權移動平均所求算的VaR值效率最好（誤差1.989%），使用歷史價格模擬法，持有期間為九日的VaR效率最差（誤差6.07%）。 預測波動度的模型部份，BGARCH較GRACH法好，但差異相當小。 本論文並建議以下的步驟，建立以VaR模式為風險控管機制的系統： 1.確立部位 2.預估該部位未來的價格風險大小（報酬變異數），預估的方法則如本研究實證中所應用的方法 3.訂定該部位預期報酬率（過去的報酬均值，或無風險利率，或直接令其為0） 4.決定該部位的持有期間（如隔夜） 5.決定要求財務安定的程度，即決定最大可能損失的信賴水準。越傾向安定的財務系統，信賴水準越高。 6.以第2-5步驟的資料計算該部位的VaR值，公司以此VaR值為標準，提列損失準備。 7.建立一套資訊系統，隨時監視部位損益與VaR的差距，如果部位損失超過VaR值應立即停損出場，不可猶豫。因為如果不停損可能產生遠超過公司提列的損失準備，使公司面臨嚴重財務危機。

確保保險公司之清償能力是保險監理單位之首要目標，監理單位使用各種不同的監理制度以確保保險公司的財務體質，並防止保單持有人因為保險公司失去清償能力所遭致之損失。在各種監理制度中，RBC監理制度主要是衡量保險公司的資本適足性並且提供監理單位採取相關監理行動的準則；VaR監理制度則是目前銀行業之監理所嘗試採取的新監理方式，而且VaR也被廣泛運用在銀行內部的風險管理系統中，由銀行監理的發展趨勢看來，可以預期保險監理將來也會以VaR監理制度為主。 本研究的主要目的在於探討VaR監理制度適用在保險監理制度上的可行性以及與現行RBC監理制度的比較。在探討VaR監理制度的可行性前，本研究先就VaR監理制度運用在保險監理的前提以及影響保險公司失去清償能力的原因進行探討。 在瞭解影響保險公司失去清償能力的原因後，本研究分別對於在VaR監理制度下保險公司如何分別針對各種不同的風險因子決定所需持有的資本額度。經過相關文獻的探討以及考慮保險業的行業特性，本研究建議市場風險與核保風險可以用VaR計算其資本額度；信用風險由於尚未有十分完善的量化模型，所以本研究建議應以徵信方式因應此一風險，而業務風險則是以規定一固定比率的資本額度因應之。本研究也建議待保險公司累積足夠的VaR使用經驗後，保險監理制度可以開放使用預先承諾法。 在運用VaR於保險監理上時，本研究也建議監理單位必須注意有關VaR的實行風險與模型風險的影響，同時也強調監理單位的檢核與市場制度的力量是VaR監理制度能夠充分運作的必要條件；此外，由於制度實施的初期，無法驗證模型與資料的可用性，所以仍必須輔以最低固定比率的要求，以確保保險公司的清償能力。 在探討VaR運用在保險監理制度上的可行性後，本研究將進一步比較VaR與現行RBC監理制度的比較。本研究主要是由制度實行的難易程度、衡量資本適足的準確性，以及監理的成本三方面進行比較。制度實行的難易程度主要是比較VaR與RBC制度的複雜度與可行性，以及與公司內部風險管理和全球金融監理趨勢的整合程度。衡量資本適足的準確性主要是比較二種制度何者更可以衡量保險公司所面臨的各種風險、清償能力的效力，以及保險公司投資組合的風險分散效果。至於監理的成本則可分為監理者、保險公司與社會成本三方面來探討。 透過本研究的比較結果發現VaR監理制度除了在制度的複雜度與可行性較RBC制度差以外，其他項目皆優於RBC監理制度。除此之外，VaR與RBC都各自有其監理上的道德風險。本研究建議如同銀行監理一般，保險監理制度應朝向VaR監理制度的趨勢前進，以更可以確保保險公司的清償能力以及投保大眾的權益。 / Assuring insurance company solvency has always been the focal point of insurance regulation. Regulators use various methods to promote insurers' financial strength and protect policyholders from losses due to insolvency. Among these methods, risk-based capital (RBC) is used to measure the insurer's capital adequacy and provide the relative action rule for the regulator, and the VaR (value-at-risk) regulation is new regulatory type the bank regulator attempt to adopt. Besides the regulatory application, VaR is also used in bank's risk management system broadly. We can expect the VaR-type regulation will be the new insurance regulation in the future according to the development of bank's regulation. The methodology of this study adopt is literature review. The most important purpose of this study is to explore the feasibility of VaR-type insurance regulation and compare the VaR regulation with current RBC regulation. Before the regulation system examination, this study firstly discusses the presupposition of the VaR regulation application and the causes of insurer insolvency. For the purpose of developing the VaR-type capital requirement in insurance regulation, this study proposes that market and underwriting risk capital requirement can be directly calculated in VaR; credit and business risk capital requirement should be regulated a fixed-rate capital amount. This study also proposes the application of precommitment approach when the regulator assure the insurer accumulate good experience in VaR. In addition, this study also addresses some points for attention of VaR insurance regulation. The other purpose of this study is to compare the RBC and VaR through the regulatory implementation, solvency measurement, and regulatory cost. The result of this study indicates that VaR is superior to RBC in any aspect, besides the complexity and feasibility. In addition, VaR and RBC both have their own regulatory moral hazard. This study suggests VaR should be used in the insurance regulation as other financial regulation in the future.

本文嘗試利用涉險值（VaR）的估計來衡量投資組合風險和規模效果之間的關係。在歷史模擬法、變異-共變異法及極端值法估計VaR的結果中，皆得到小規模策略投資組合之可能損失風險額大於大規模策略投資組合。由VaR的估計，我們可得以下結論：規模溢酬和風險具有高度相關。小規模策略投資組合的風險高於大規模策略投資組合，故需具備較大規模策略投資組合為高之風險溢酬。 而投資人若進行買進小規模策略投資組合及賣出大規模策略投資組合，則因所承擔之風險較高，故所獲致優於大盤的績效，便在於彌補其所承擔的風險。此結果支持理性資產定價模式（Rational Asset Pricing）的論點。

Artzner等學者在1999年提出風險測量值應具備同調（coherent）性質，然而，涉險值並未能完全符合。本文針對Wirch ＆ Hardy（1999）提出滿足Artzner et al.（1999）所定義同調性質之風險量化指標如條件尾端期望值（Conditional Tail Expectation；又稱尾端涉險值，Tail-VaR）以及危險比例（proportional hazards；PH）、雙重次方（dual power；DP）變形函數（distortion function）等風險衡量方法作探討，參考MGWP（1980）、Boyle ＆ Hardy（1997）、Hardy（2000）、Yang（2001）、Wilkie ＆ Waters ＆ Yang（2003）對於附保證給付之投資連結型保險契約提存準備金的方法，將其應用到保險公司所發行的附保證給付之風險量化上，同時比較其與涉險值之差異。其中之數值分析將以附最低死亡保證給付（Guarantee Minimum Death Benefit）之變額年金，以及附保證年金選擇權（Guaranteed Annuity Options）之單位連結（Unit-linked）保險商品作為範例，分別以台灣、英國兩地的投資環境為背景，檢視其附保證給付之投資型保單可能面臨的風險暴露，提供保險公司作為提存投資型商品保證給付部分之責任準備金參考。 / In this paper we introduce the properties of a coherent risk measure（Artzner et al（1999））. The risk measure of Value at Risk that does not adhere to the consistency requirements is discussed. We consider the coherent risk measures of conditional tail expectation（also known as Tail-VaR）, proportional hazards and dual power distortion functions outlined by Wirch and Hardy（1999）. MGWP（1980），Boyle and Hardy（1997），Hardy（2000），Yang（2001），Wilkie, Waters and Yang（2003）use VaR and the latter two papers also apply conditional tail expectation to reserve for investment-linked contracts with guaranteed risk. Instead, we apply the coherent measures to reserve two different types of guarantee：guarantee minimum death benefit and guaranteed annuity options attached to variable annuity contracts and unit-linked contracts separately. In addition, the comparison of the numerical results for VaR risk measure and coherent risk measure are analyzed.

由於許多資產報酬率的分配呈現厚尾的現象，因此，本文探討將最低報酬要求限制條件加入傳統的平均數╱變異數模型中，考慮在分配已知的情形下，假設資產報酬率的分配為t分配及常態分配，來求取最適的資產配置；在分配未知的情形下，利用古典Bootstrap法、移動區塊Bootstrap法及定態Bootstrap法的抽樣方法來模擬資產報酬率的分配形式，並利用模擬的資產報酬率分配求出最適的資產配置。 同時，本文亦探討資產配置在風險管理上的運用，當分配已知時，若對分配參數的估計正確，則使用的最低要求報酬率就是此資產配置的涉險值，反之，若對參數的估計錯誤時，會對資產配置產生很大的影響及風險管理上的不正確；當分配未知時，利用模擬方法來產生分配，則使用的最低要求報酬率可看成是此資產配置的涉險值。 實證部分選取資料分成本國及全球，研究發現對於何種分配或模擬方法的資產配置績效最好？沒有一定的結論。其原因是各種分配或模擬方法皆必須視資料的性質而定，因此，本論文的貢獻僅在建議使用厚尾分配及利用模擬方法，來符合資產報酬率呈現厚尾的現象，並利用此分配，以期在考慮最低報酬要求限制條件下的資產配置更為精確。 / The distributions of many asset returns tend to be fat-tail. This paper attempts to add the shortfall constraint in Mean-Variance Analysis. When the distribution is known, we find the optimal asset allocation under student-t distribution and normal distribution. On the other hand, we use Classical Bootstrap, Moving Block Bootstrap, and Stationary Bootstrap to stimulate the distribution of asset return, and to obtain the optimal asset allocation. We also examine the risk management of asset allocation. When we use the correct estimators of parameters under the known distribution, the threshold in shortfall constraint is the value-at-risk in asset allocation. Otherwise, if using the wrong estimators, we get the incorrect asset allocation and the improper risk management. When the distribution is unknown, using simulation to generate the distribution, the value-at-risk is the threshold. The empirical study is conducted in two parts, domestic and global asset allocation. The results cannot point out which distributions and simulations are suitable. They depend on the data’s property. The contribution of this paper is to introduce some methods to fit the fat-tail behavior of asset return in asset allocation.

確保保險公司的清償能力一直是保險監理的重心。在所有施行的保險清償監理工具中，風險基礎資本（Risk-Based Capital, RBC）是目前為止最先進的代表。然銀行監理機關已經推薦涉險值（Value at Risk, VaR）系統為資本適足要求的工具，因此涉險值有很大的潛力成為下一代的保險資本適足要求工具，雖然尚未施行。由於保險監理的重要性以及RBC和VaR在其中扮演重要的角色，兩者相對上的精確性是我們所感興趣的。 本篇論文的目的是實際去比較RBC及VaR在破產預測上的相對精確性。我們以美國1995到1998年產險公司的實際清償記錄，用型1及型2錯誤檢視RBC及VaR的破產預測能力。RBC的數據直接從產險公司報給NAIC的年報上就可取得，而VaR的數據來自於我們所建立的現金流量模擬模型。既然RBC的數據是實際的數據，而VaR的估計值也是基於公司實際的財務數據而來，我們能以實例展現VaR相較於RBC的財務預警能力。 我們的結果顯示RBC沒有任何財務預警能力，換句話說，沒有一個破產公司的RBC值小於0.7（監理機關可以根據這個值關掉公司）。另一方面，VaR有較好的財務預警能力，但是它同時也會使許多財務健全的公司必須接受許多沒有必要的檢查。我們VaR模型的整體正確分類能力只比隨意分類稍微好一些。 雖然結果並不如原先預期的好，我們仍然對VaR成為保險監理工具抱持樂觀的態度，因為它是目前為止最嚴密也最先進的風險管理工具。我們認為這些結果可以藉由修正不適當的假設後獲得改善，未來研究可以先朝這個方向努力。 / Assuring insurance company solvency has always been the focal point of insurance regulation. Among the employed solvency regulation methods, RBC represents the currently state-of-the-art capital adequacy requirement. Bank regulators already advocated the use of VaR systems in capital adequacy requirements. Value at risk thus has great potential to be the next-generation capital adequacy regulation, although not implemented yet. Because of the importance of solvency regulation as well as the key role played in that regulation by RBC and VaR, the relative accuracy of RBC and VaR is of great interest. The purpose of this research is to empirically compare the relative effectiveness of RBC and VaR in predicting insolvency. Through the solvency record of property-casualty insurers in the United States from 1995 to 1998, we examine the Type I and Type II error of VaR and RBC in predicting insolvency. The RBC figures are readily available from the annual statement since 1994 and the VaR values come from a simulation model that we build up. Since the RBC figures are the “real” numbers and the VaR estimates also base on the companies’ real financial positions, our research will demonstrate how VaR is compared to RBC in early warning for real cases. Our result shows that RBC doesn’t have any prediction power. In other words, none of the bankrupt insurers has a RBC ratio lesser than 0.7, the threshold according to which the regulator can seize the company. On the other hand, VaR has good early warning ability, but also leads the regulator to take too much unnecessary actions on solvent companies. The overall ability of correct classification of our model is just a little stronger than arbitrary classification. Although our results are not as good as we expect, we are still optimistic about the use of VaR, the currently most comprehensive and advanced approach of risk management, as an insurance solvency regulation tool. We attribute the unsatisfactory outcome to some assumptions that may be inappropriate. Further researches can move toward this aspect.

中文摘要 在本文中，我們依據模擬的風險因子變動，包括死亡率風險，利率風險，解約率風險以及模型的參數風險，來估計第一個保單年度的期末責任準備金之涉險值 (Value at Risk)。本文中，雖僅計算生死合險保單的準備金之涉險值，但是本文所提供的方法以及計算過程可以很容易的應用到其它險種，甚至配合資產面的考量來計算保險公司盈餘(Surplus)的涉險值，進而作為清償能力的監測系統。 本文的特點包括下列幾項：第一，本文提供了一個不同於傳統短期間(Short Horizon)的涉險值計算方式，來估計壽險商品的保單責任準備金(Policy Reserve)的涉險值。第二，本文利用生命表來估計死亡率風險所造成的涉險值。第三，我們利用隨機利率模型來捕捉隨機利率對於責任準備金涉險值的影響。第四，我們考慮解約率對於責任準備金涉險值的影響，值得注意的是，在我們的解約率模型中，引入的利率對於解約率的影響。第五，本文亦考慮風險因子模型當中的參數風險對於涉險值的影響。最後，我們利用無母數方法計算出涉險值的信賴區間，而信賴區間的估計在模擬過程當中尤其重要，因為它可以用來決定模擬次數的多寡。 本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。 本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。 / ABSTRACT In this paper, we estimate the VAR of life insurer's terminal reserve of the first policy year by the simulated risk factors, including mortality risk, interest rate risk, lapse rate risk, and estimation risks, of future twenty years. We found that the difference between the VAR under the mortality risk and the interest rate risk is very large because interest rate is a stochastic process but not mortality rate. Thus, the dispersion of interest rate is more then mortality rate. In addition, the VAR will reduce a lot after adding the impact of lapses because the duration of the reserve reduced. If we neglect the impact of lapses to VAR, we will overestimate the VAR significantly. The features of this paper are as follows. First, we provide an approach to measure the VAR of a life insurer's reserve, and it is rather different from traditional VAR with short horizons. Second, we use mortality table to estimate the VAR of a life insurer's reserve. Third, we use stochastic interest rate model to capture the effect of random interest rate to the VAR of a life insurer's reserve. Fourth, we relate the future cash outflows to interest rate and produce a reasonable estimator of VAR. Fifth, we consider the effect of estimation errors to the VAR of a life insurer's reserve. Last, we calculate the confidence interval of the VAR estimates of the policy reserves. This paper consists of six sections. The first section is an introduction. In the second section, we present the method used to estimate the variance of the mortality rate and then estimate the VAR of reserves from these variances. In the third section, we explore how to use stochastic interest rate model to estimate the reserve's VAR and the VAR associated with the parameter risk of the interest rate model. In the fourth section, we analyze the contribution of the lapse rate risk and the parameter risk of the lapse rate model to the reserve's VAR. We also analyze the relative significance of the interest rate risk, the lapse rate risk, and the mortality rate risk in terms of their marginal contributions to the VAR of an insurer's reserves in this section. In the fifth section, we calculate the confidence intervals of the VAR estimates discussed in the previous sections. The last section is the conclusion section containing our conclusions and discussions about potential future researches.

保險公司清償能力一直是保險監理的重心，在所有現行的制度中風險基礎資本是最重要的，但此項制度仍有其缺點，因此其他動態分析模型被許多學者所提出，如涉險值及情境分析。雖然這些動態分析模型被學者所偏好，但監理機關仍須對這些模型的精確程度加以了解，這也是本篇論文所要研究的目的。 基於此，本篇論文以模擬方式及經濟模型加以分析風險基礎資本、情境分析及涉險值等方法的破產預測的相對精確性。其中風險基礎資本完全採用現有NAIC的年報資料，情境分析及涉險值則採用我們所建立的模型，基於此也可以確認現有監理制度是否有缺失。 我們的結果發現風險基礎資本的預測能力很低，動態模型-情境分析及涉險值皆優於風險基礎資本，且在不同動態模型中涉險值的預測能力較好。因此可知被學者所偏好的動態分析模型應是未來保險監理的方向希望藉由本篇提供監理機關一個參考的依據。 / Solvency prediction of insurers has been the focus of insurance regulation. Among the solvency regulation systems, risked-based capital (RBC) is the most important but RBC still has some drawbacks. Thus, the dynamic financial analyses-scenario analysis and Value at Risk have been developed to be the regulation tool. Although, the scholars prefer the dynamic financial analysis, the regulators still want to make sure the accuracy of dynamic financial analysis. That is the purpose of our paper. Therefore, we use the simulation result and the econometric model to analyze the relative effectiveness of RBC, scenario and Value at Risk (VaR). The RBC is from the annual statement and the scenario and VaR come from our simulation model. Our result shows that the RBC has very low explanatory power, the dynamic financial analysis is better than RBC, and VaR outperform scenario analysis. Thus, we conclude that VaR is the way to go for property-casualty insurance regulators.