| Abstract: | 保單失效率(Lapse Rate)是評估保單品質的重要指標，對保險公司的影響也相當深遠。例如，當保險公司實際評估其準備金適足性以確認保單未來現金流量足以支付可能發生的給付時，通常都會根據其以往的經驗，針對各保單年度所可能發生的失效率做適當的假設，以進行評估。此外，當保險公司進行保單定價時，也會根據類似的失效率假設，以便評估保單的利潤率。因此保險公司有必要深入瞭解保單失效率的動態行為，尤其是「失效率期限結構」的動態行為。「失效率期限結構」（the term structure of lapse rate）指的是保單失效率會隨著保單年度的不同而呈現出特定性質的現象。一般而言，失效率會隨著保單年度的經過而遞減，所以保單在發行後的第一年間會有比較高的失效率，然後就會逐年遞減。 Kim (2005)發現韓國的保單失效率具有這個特性。此外，根據中華民國人壽保險商業同業公會所做的有關失效率的研究統計結果，我們也發現台灣的保險市場也有此現象。本研究決定採用利率期限結構相關文獻中常用的隨機模型進行「失效率期限結構」動態行為的研究。在第一年的計畫中，我們利用主成分分析法（Principal Component Analysis, PCA）來估計影響失效率期限結構資料的重要因子。接下來，我們參考Chen, Roll, and Ross (1986)的方法，分析那些總體經濟變數可能影響失效率期限結構的動態行為。最後，根據Litterman and Scheinkman (1991)的建議，我們利用複製投資組合（mimicking portfolios）的觀念，透過利率的期限結構來複製規避失效率波動風險的避險組合。在第二年的計畫中，我們將利用兩個無母數統計方法來估計整條失效率期限結構。這兩個方法分別為Nelson-Siegel 模型以及Svensson 模型。這兩個模型在利率期限結構文獻中常被用來估計殖利率曲線。雖然這兩種模型可以相當又彈性地進行估計，卻仍屬於靜態而被動的估計殖利率曲線，因此與我們想進一步了解失效率曲線動態行為的目的不吻合。所以我們決定採用Diebold and Li (2006)的方法來描述失效率期限結構的動態行為。Diebold and Li 的作法是先針對每一條殖利率曲線配適 Nelson-Siegel 模型，然後在根據每個模型的參數配適其最佳時間序列模型，期能透過這些模型來預測每個參數的動態，進而預測整條殖利率曲線未來的動態行為。換言之，透過Diebold and Li 的模型，我們可以預測整條失效率曲線的動態行為。估計完整條失效率曲線的動態行為後，我們也嘗試透過Willner (1996)所建議的方法，利用 Nelson-Siegle 模型來討論如何規避失效率所造成的現金流量風險。由於保險文獻中關於失效率動態行為的研究相對稀少，加上缺乏個別保單年度失效率的相關統計資料，就我們所知，目前文獻中根本沒有「失效率期限結構」動態行為的相關研究。因此，本研究具有一定程度的學術貢獻度。除此之外，本研究的成果亦可協助保險公司精確的評估其準備金適足性以及保單利潤率，所以本研究也具有相當程度的實務應用性。
Understanding the dynamics of the lapse rate is crucial to insurance companies. First, the pricing of an insurance policy is dependent on the dynamics of the lapse rate. Policy lapse may make the insurance companies unable to fully recover their initial expenses, including the cost of procuring, underwriting, and issuing new business. Hence, the insurance companies may incur losses from lapsed policies. Second, the evaluation of reserve adequacy of an insurance company is usually conducted under a presumed dynamics of lapse rate. Third, since the returns of the assets in which an insurance company invests and the lapse rate are both interest-rate-dependent, the dynamics of the lapse rate is also an important factor to the success of the asset-liability management of an insurance company. Therefore, the dynamics of the lapse rate, especially that of the term structure of lapse rate, is of great importance for an insurer’s liquidity and profitability. Similar to the term structure of interest rate, which illustrates the relationship between interest rates and term to maturity, the term structure of lapse rate describes the relationship between the lapse rate and the policy year of an insurance contract. Kim (2005) find that there exists a convex term structure of lapse rate in Korean insurance market. In other words, the lapse rates decrease as the policy age increases. We observe a similar pattern of the term structure of lapse rate in Taiwan. According to Taiwan Standard Ordinary Experience Mortality and Lapse Rate Report published by Life Insurance Association (LIA-ROC), the lapse rates of various insurance policies also decline as the policy age increases. This paper adopts the stochastic models in the literature of the term structure of interest rates to study the dynamics of the term structure of lapse rates in Taiwan. In the first year of this two-year research project, we follow Litterman and Scheinkman (1991) to employ principal component analysis (PCA) to extract underlying latent factors of the term structure of lapse rates. Next, we adopt the methodology of Chen, Roll, and Ross (1986) to relate these factors to some macroeconomic variables. Finally, we attempt to construct the mimicking portfolios of these underlying factors based on interest rates of different terms to maturity. These mimicking portfolios are important because it is possible for insurance companies to hedge the risks caused by the shifts of the term structure of lapse rates through them. In the second year, we decide to utilize two commonly used non-parametric methods, Nelson-Siegel model and Svensson model, to describe estimate the shape of the term structure of lapse rates. Although these two models have been proven useful in describing the shape of the yield curve, they can be classified as static models that are not able to properly illustrate the dynamic behavior of the yield curve. The same reason is equally applied to the dynamic behavior of the lapse curve. Therefore, we decide to take up the method proposed by Diebold and Li (2006) to describe the dynamics of the term structure of lapse rates. Diebold and Li begin by estimating the parameters of Nelson-Siegel model for every yield curve and then examine the dynamic behavior of the parameters by fitting various time series models, e.g., the ARIMA models and the error-correction model. If some time series models can satisfactorily fit the time series of these parameters, then it is possible to forecast them in advance and the whole yield curve. In other words, if we are able to successfully estimate the term structure of lapse rates based on Diebold and Li’s method, we have a chance to forecast the future behavior of the lapse curve. After this, we also attempt to follow the method of Willner (1996) to explore the possibility of hedging the cash flow risk caused by the lapse behavior of policyholders based on estimated Nelson-Siegel model. Despite of the obvious importance of lapse rate, there is a paucity of academic research on its dynamics, not to mention the dynamics of the term structure of lapse rate. As a matter of fact, to the best of our knowledge, this paper is the first rigorous study of this topic. This is the major contribution of this paper. Because the empirical results of this paper would be useful for the insurance companies to evaluate their reserve adequacy and pricing correctness of policies, this paper also has significant practical contribution to the insurance industry. |
