1970 至 1980 年代初期，美國壽險業在高市場利率的衝擊下，壽險保單持有人為尋求更高的投資報酬，紛紛提出解約(Lapse)或保單貸款(Policy loans)的要求，產生所謂的脫離金融機構症(Disintermediation)，此現象可能造成保險公司現金大量流出，進而影響公司的資金運用。故美國壽險公司為降低此種利率不正常變動所造成之影響，便致力開發變額壽險等與利率相關的保單商品。 人壽保險契約解約率(Lapse rate)過高一直是壽險公司經營上的困擾，解約率的高低除直接反應保單的穩定性外，亦可作為公司業務成長及業務品質的重要指標。我國對於影響壽險契約解約率因素的研究多以問卷調查的方式為之，藉此瞭解個別保戶解約的動機，屬個體面的探討，此種研究方法可能無法直接反映總體經濟環境的改變所造成的影響。由歐美國家學者提出的相關研究，顯示其已漸漸重視總體經濟環境興壽險解約率間的相互關係。反觀國內並無相關的研究文獻，故本論文即以壽險解約率與總體經濟關係為研究的主題。 本論文的實證研究受限於國內壽險業發展較晚及資料取得不易，故以成立時間較久的七家本土壽險公司為研究樣本，以民國 72 年至 85 年為研究期間，被解釋變數則分為保額解約率及件數解約率兩項，解釋變數為經濟成長率、平均每人國民所得、替代資產報酬率、失業率及通貨膨脹率。並以橫斷面及時間序列結合資料(Panel data)型態應用於壽險解約率的模型建構，此資料型態可解決壽險解約率相關資料太少，無法有足夠樣本建構橫斷面或時間序列資料型態的模型，故本研究採用此種資料探討壽險保單解約率與總體經濟變數間的關係，並透過各種檢定方法，選取解約率模型。 實證結果顯示國內經濟成長率及平均每人國民所得對壽險保額解約率及件數解約率皆有顯著的影響，失業率在轉換前的件數解約率模型為顯著，替代資產報酬率及通貨膨脹率皆不顯著。此實證結果可能因變數選取的不適當而扭曲，但壽險公司仍可根據本研究的研究方法，修正有關的解釋變數建立適合公司的解約率模型，提供壽險公司擬定相關策略，降低總體經濟變動對壽險公司解約率的衝擊。 / Lapse rate plays a crucial role in monitoring the effectiveness of management for life insurers. Its changing phoneme not only characterizes the stability of the insurer's financial strength but also provides a benchmark in valuing the development and quality of business. There are many factors influencing the lapse rate of the life insurance policies. In this study, macroeconomics index, economic growth rate, per capita income, rate of return on alternative, unemployment rate and inflation rate are selected as independent variables to measure their importance. Seven Taiwan domestic life insurers between 1983 and 1996 are sampled and studied. The panel data approach combining cross sectional and longitudinal observations are adopted. The lapse rate of the insured amount and the insured case are selected in variable intercept regression model as dependent variable to summarize the mutual relationship with the chosen independent variables. F-tests, Lagrangian-multiplier test and Hausman test are performed in making the conclusion. Based on our study, several results have been found and summarized as following. (1) Economic growth rate and per capita income are found to be significant in influencing both the lapse rates of insured amount and insurance case. (2) Unemployment rate is also significant in influencing the lapse rate of insurance case. (3) There is no significant effect from the rate of return on alternative and inflation rate. This study has emphasized on employing the methodology of adopting the panel data to explore the relationship between the lapse rate and the selected macroeconomics factors. Based on our approach, the life insurers could monitor its renewal life insurance policies and associated cash flows when the impacts from the macroeconomic factors present.

本篇論文要探討的主題為何種總體或個體因素會影響投保人在壽險上的解約行為。由於壽險保單的解約行為會讓保險公司面臨現金流、聲譽、逆選擇等風險，進而影響公司營運。因此探討影響保單解約率之因素，進而準確估計保單的解約率為十分重要的議題。此外，不論投保人主動解約或是被動使保單失效均會對保險公司造成影響，因此本篇論文也將利用不同解約率的計算方式進行實證分析，研究是否不同計算方式的解約率會影響實證結果。本文使用NAIC (National Association of Insurance Commissioners)保險資料庫之年報資料，對2004-2014年間保險公司之經營狀況進行分析，驗證解約率實證中常用的三個假說：市場利率假說、緊急資金假說以及保單替換假說，選用之變數包含失業率、利率、保單替換率、高齡比等變數，並採用固定效果模型作為縱橫資料之迴歸模型，分別對不同計算方式所得之解約率進行迴歸分析，並比較彙整其結果。最後針對結果提出未來研究之建議。 / Insurance companies’ business will be influenced by surrender activities in several aspects, such as cash flow problem and inverse selection problem. Empirical researches show that both macroeconomic variables and microeconomic variables will influence surrender behaviors. Hence, this paper seeks to which kinds of macroeconomic variables will influence surrender activities and investigates whether using different ways to calculate surrender rate will cause different empirical results. All available US insurance company data, ranging from January 2004 to December 2014, are obtained from the annual statement in NAIC (National Association of Insurance Commissioners).We found some evidence supporting Emergency Fund Hypothesis and Interest Rate Hypothesis, but using different ways to calculate surrender rate may cause a little bias in conclusion. However, the relationship between surrender activities and macroeconomic variables supports insurance companies to understand and actively manage lapse/surrender risk.

責任準備金的風險管理是人壽保險公司營運的重要課題之一，其牽涉到保單現金流量的數階動差及分佈之估計，為此我們必須清楚的設定隨機脫退和隨機利率模型，並將保單之重要特性—利率敏感性現金流量納入考慮，否則將誤導保險公司過度規避利率風險及高估其破產的危險性。 本文採用蒙地卡羅模擬法進行責任準備金的模擬，在模擬模型中考慮三個風險因子：死亡率風險、利率風險和解約率風險。透過死亡率的變異數估計死亡率風險對責任準備金的影響；透過隨機利率模型估計隨機利率對責任準備金的影響；於解約率模型中考慮利率與解約率的關係，估計解約率對責任準備金的影響；當中並將隨機利率模型與解約率模型的參數風險納入考慮。最後，將五個險種的現金流量加權平均，以建構保險商品組合，而具有最小的最大分散（maximum dispersion）的保險商品組合即為最佳商品組合，所謂責任準備金的最大分散即責任準備金之第95個百分位數與其平均數之差距。 由模擬結果發現，保險公司應密切注意其責任準備金之利率風險管理，但這並不表示保險公司可忽視解約率風險對責任準備金的影響，而過度規避利率風險，此模擬結果幫助保險公司評估其業務之風險。 / One of the major topics in insurance companies’ operations is the risk management of the reserves. Sound risk management of reserves involves the estimation of the moments and distribution of cash flows associated with sold policies. To estimate the moments or the distribution of future cash flows, one must model stochastic decrements and stochastic discount rates explicitly. Besides, one must consider an important feature of insurance policies: future cash flows may be interest-rate-sensitive. Ignorance of such characteristic may mislead the insurer to over-hedge the interest rate risk and jeopardize the solvency of insurers. In this paper we use Monte Carlo simulation to estimate reserve. We identify three risk factors embedded in life insurers’ reserves in our simulation model: mortality risk, interest rate risk, and lapse rate risk. We use the mortality risk to decide the reserve from the variances of mortality rates. We choose a term structure to decide the reserve from the interest rate risk. Furthermore, we incorporate lapse rate risk into the decision of reserve by recognizing the relationship between lapse rates and interest rates. We also estimate the parameter risk associated with the parameter estimation errors in the term structure model and the lapse rate model. Finally, we construct insurance portfolios by summing weighted cash flow of five insurance policies. According to the minimum maximum dispersion, we intend to find the optimal portfolio and identify that the maximum dispersion of the distribution of terminal reserve is the difference between reserve’s 95th percentile and mean. We find that the maximum dispersion generated from mortality risk is insignificant while maximum dispersion from interest rate risk is substantial. This result is consistent with the observation that life insurers suffer more from the interest rate risk than from the mortality rate risk. The marginal contribution of lapse rate risk to the maximum dispersion, surprisingly, is negative. One possible reason is that the duration of the reserve decreases if policies lapse and lower duration means less interest rate related risk. This seemingly surprising result implies that we would overestimate the maximum dispersion if we neglect the lapse rate risk. We also find that the parameter risks of the interest rate model and the lapse rate model are significant. Our findings suggest that life insurers should pay close attention to interest rate risk management. However, be careful not to neglect the effect of lapse rate and over-manage the interest rate risk. In addition, insurers should be aware of the significance of parameter estimation risks in pricing models. The results of portfolios show that the maximum dispersion is deeply affected by the considered risk and the diversification effect. Our results can help life insurers to access the riskiness of their business.

解約風險為壽險公司承保風險中最重要之風險，文獻指出若於保單定價時忽略解約率可能為動態，將影響壽險公司損益、資產配置、資金流動性及風險管理計畫。本研究將以保費及準備金試算進行實證研究，觀察以傳統精算方式定價(忽略解約率為動態)將對保費及準備金之計算造成多少誤差。 本研究首先使用台灣壽險業1987年至2011年之生死合險、終身壽險解約率資料，並透過主成分分析、模擬主成分分數並將其轉回各保單年度解約率，以完成動態解約率之模擬。接著以30歲男性為對象，計算不同情境下之保費及準備金。最後比較不同情境下之保費及準備金差異以了解忽略隨機解約率對保單定價之影響程度。 實證結果顯示，考量隨機解約率與否對生死合險保費計算稍有影響但不明顯，但若長期累積觀察，是否考量隨機解約率對生死合險準備金有顯著影響。本研究使用之終身壽險解約率模型與利率無關、僅受其自身隨機效果影響，故是否考量隨機解約率對終身壽險保費及準備金之影響程度皆不大。

過去有相當多的文獻針對解約率建立模型，但由於資料取得之困難，鮮少文獻針對不同保單年度之解約率進行分析，本研究將以台灣壽險業資料分析不同保單年度之解約率行為，期望能找出解約率之期限結構，提供壽險業者訂價或風險管理之參考依據。 　　本研究使用台灣壽險業1987年至2011年間之生死合險及終身壽險資料，透過資料分析顯示兩險種之解約率關聯性不大，且應將繳別分為三類進行分析，分別為不分繳別、月繳及年繳和半年繳及季繳三類，針對各保單年度進行主成分分析，結果顯示皆需6至8個主成分方可達到90%之解釋力，並透過ARMA模型檢驗選定之主成分與總體經濟變數間之關聯性，進而觀察是否符合利率假說及緊急資金假說，最後透過VAR模型或ARMA模型模擬總體經濟變數和各主成分之分數，並利用主成分分析之結果將主成分分數轉換回保單年度變數，完成各保單年度解約率之模擬，建構出台灣壽險業解約率之期限結構。

一般而言，壽險公司會在保險契約生效前就支付保單相關之費用，例如核保與承保之成本，並且公司會預期未來保險期間內可以填補上述費用；但若保戶於保險期間內早期解約或是解約情形嚴重，將使壽險公司難達到損益兩平之目標而招受損失，影響公司預期盈收，進而增加公司資金調度上之困難。因此，對於長期穩健經營之壽險公司而言，瞭解各保險解約率變動情形對於公司之財務規劃相當重要，以期降低危害公司之風險。 本文期望藉由台灣保險事業發展中心之實證資料蒐集與相關分析，探討影響台灣壽險業生死合險及不還本終身壽險解約之因素以及其解約率之特性，進而建立與利差及保單年度相關之解約率模型，以期能準確地估計台灣壽險公司生死合險解約率與不還本終身壽險解約率。除此之外，本研究將所建構之解約率模型應用於公司未來現金流量分析，以蒙地卡羅法模擬各險種保單準備金之分配，瞭解各種解約率假設對於公司未來現金流量之影響，進而瞭解解約率參數假設對於準備金風險之評估扮演重要角色。 / In general, the life insurance companies would pay the expenses with respect to the insurance policies before the validity of insurance contracts such as underwriting and insuring costs. If the policyholders are early-surrendered or over-surrendered during the policy period, then it will make the insurance companies hard to achieve their break-even goal and result in affecting the companies’ surplus as well as management of their capital. Thus, for the long-term and stable life insurance companies, it is extremely important to understand the changes of lapse rate in order to reduce the financial risk damage before making any financial decisions. In this article, we expect to focus on the causes and the features of lapse rate changes by collecting and analyzing the empirical data of endowment and whole life insurance in Taiwan from Taiwan Insurance Institute. Based on our analysis, we could build the lapse rate model concerning the relation between the lapse rate and interest rate difference or policy year for estimating the endowment lapse rate and whole life insurance lapse rate accurately. Moreover, we apply the lapse rate model to company’s cash flow analysis. We employ the Monte Carlo simulation to simulate the policy reserve distribution, and we find out that the lapse rate assumption plays an important role in the policy reserve evaluation.

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.