The Alternative Pricing Approach for Variable Life Insurance Incorporating Secondary Life Insurance Market

Abstract

變額壽險保單主要特點為保早到期給付金額連結於投資標的資產之市場價格，因保單所附保證收益可視同賣權價值，典型評價模式即結合現代財務選擇權理論與傳統壽險精算等價原理，文獻上後續的相關研究皆沿用此計價原則。由於近年來美國壽險保單次級市場的快速發展與成長，使得壽險保單在市場交易的流動性大為增加，壽險保單已不單是為獲取保障的保險契約，亦是可交易的資產組合，此市場特徵提供了應用財務選擇權計價模式的重要條件，因此，有別於上述傳統典型的計價方法，本研究以純粹的財務選擇權定價觀點，特別納入壽險次級市場因素，針對變額壽險保單提出另一種計價核式，並以此觀點檢視變額壽險保單的傳統計價方法及其特性。在本研究的計價架構下，除証明了傳統計價方法所求得之價格將對應一組特定的風險中立測度外，數值分析結果亦說明了無套利的合理價格與傳統計價結果的關係，結果顯示，保單的無套利合理價格範囝將因連動資產價值的波動性、無風險利率及死亡機率型態之改變而呈不同方向的變動，尤其會隨著壽險保單在次級市場的流動性風險溢酬增加而擴大。

One distinguishing feature of variable life insurance policy is that the benefit payable at expiration depends on the market value of the linked reference portfolio as contrasted with traditional life insurance policies. The conventional pricing approach combines traditional law of large number considerations and financial mathematics. Subsequent relevant studies follow such the valuation approaches. Because recently secondary life insurance markets in America are developing and growing rapidly, liquidity of life insurance contracts has significantly improved. So life insurance contracts could not only be guarantees against losses, but also could be seen as tradable portfolio assets. This market characteristic could serve an extra condition for the application of option pricing model to the valuation of variable life insurance. In this article, in comparison with the conventional pricing approaches for variable life insurance, an alternative valuation method is developed with pure option pricing approach especially incorporating the secondary life insurance market. The conventional valuation approach and its properties are reviewed and its derived price is proved as a special one with respect to a specific risk-neutral probability measure in the present valuation framework. Numerical analysis illustrates the relationship between no-arbitrage price bounds and the conventional pricing approach as well. The results indicate that no-arbitrage bounds of the insurance contract would be influenced by asset price volatility, risk-free rate and mortality pattern in different directions, and particularly would be augmented with liquidity risk premium in the secondary life insurance market.