PricingMortalitySwapwithMortalityCorrelationRisk

[[abstract]]摘要 本文主要建立死亡相關模型與死亡相關證券化。根據實證文獻之結果，選取影響死亡率的三項因素(性別、年齡和收入)作為被保險人存活率模型的因子，進而求出其死亡機率。再者，藉由可將個別邊際機率合成為聯合機率的Copula Function 捕捉個別壽險間的死亡相關性 (意即被保險人間的死亡相關性)。最後，設計一個可以提供規避死亡相關風險之新金融商品，本文稱之為第一次死亡交換商品(First – to - Death Mortality Swap)，並且給予定價以及數值分析。 Lin和Cox (2005)提出死亡率風險證券化及評價了死亡債券及死亡交換，並且做了以下假設。首先，被保險人間的死亡率分配是獨立的。第二，死亡債券及死亡交換的所連結的年金保險具有相同的本金。最後，死亡債券和死亡交換之連結標地為全體的死亡風險，這暗示了有不同的風險偏愛的債券或交換投資者面臨了相同的死亡風險。然而，事實上，保險人的死亡率具有相關性。例如，被保險人是相同的年齡層，則他們的死亡相關性就越高，因此被保險人間的死亡率是相關而不是獨立。因此，對保險公司而言，死亡率的相互關係扮演著很重要的角色。為了改進上述問題，本文設計了另一個死亡率連結的金融商品-第一次死亡交換商品(FTD-MS)。FTD-MS為一連結多個壽險保單之投資組合。被保險人的收入相關性可視為死亡保險單相關性的代理變數。針對死亡保險單的相關性，本文藉由可將個別邊際機率合成為聯合機率的Copula Function 來捕捉。[[abstract]]Abstract The purpose of the article is to study the securitization of mortality correlation risk. Firstly, a mathematical function that combines marginal probability into a joint distribution, Gaussian and t-Student copula, are used for the correlation of multiple life insurance policies. Further, according to the empirical results, this paper first models the stochastic morality intensity and then choices three important risk factors (gender, age, income, and other factors) which affect mortality rate to derive the survivor probability for the policyholder. Finally, the innovative product called First-to-Death Mortality Swap (FTD-MS), is designed, priced, and report the numerical results. Lin and Cox (2005) propose the securitization of mortality risks and price mortality bonds and swaps with embedded mortality options, and assume that the mortality distributions of policyholders are independent. Nevertheless, it makes the intuitive sense that the mortality risk of policyholders should be correlated. Hence, for the insurers, mortality correlation risk also plays an important role and the mortality correlation risk should also be emphasized. Consequently, in practice, the joint mortality probability should be projected accurately in hedging or pricing the securitization of mortality risk. To improve the above problem, firstly, this paper takes mortality correlation between the policys into account. We assume that income correlation of multiple policyholders is used as a proxy for the correlation of multiple mortality insurances. For the correlation of multiple mortality insurances, this paper uses a copula function, which is a mathematical function that combines marginal probability into a joint distribution. The common copula in this family of distributions is the Gaussian one. In addition, we also uses t-Student copula which has upper tail dependence to catch the phenomenon for heavy tail distribution of the income. Secondly, we will design and price an alternative mortality-linked security called FTD-MS which linked to a portfolio of life insurance with the same insurance amount and correlation matrix between the policys