This study focuses on the management of the three most challenging topics life insurers in Taiwan currently face, namely the life insurance policy with the highest annual
gross premium income, the dominating asset on the life insurer's balance sheet, and the development of a model which faithfully captures the dependency between multiple
underlying assets within the life insurer's portfolio. We first examine the fair pricing of interest rate sensitive life insurance policies that are commonly sold in Taiwan. With the reference portfolio following Heston's stochastic volatility process, the payoff function of these policies consists of a series of forward-start options. Although the option to surrender are standard features of these policies, policyholders incur heavy penalties should they exercise such option. Given certain policyholder behaviour, we study the impact of the minimum guaranteed interest rate, and the annually declared bonus rate on the issuing company's solvency. The need for pricing transparency and a reliable source of reference is of utmost importance in view of the sheer volume of the international bonds listed on the Taipei Exchange that the life insurers in Taiwan hold and the lack of a liquid secondary market. We provide the life insurers the means to evaluate the mark-to-market value of these callable bonds without having to rely on third parties to do so. We are able to collate publicly available data and make use of open source software to construct a bespoke system that can independently price the international bonds. The copula concept with its multivariate time-series model generalization, namely the copula-GARCH model, and robust statistical inference procedures based on the empirical processes theory are investigated in depth. A vast majority of existing literature on applications of copula often makes assumptions without justification or conducts inadequate statistical tests for verification. Here we demonstrate what we believed to be the preferred way of using copula for financial and risk management applications by the detailed valuation of guarantees embedded in variable annuities with multiple underlying assets.
本研究由三篇關於保險業資產負債管理議題的論文所構成。本文第二章檢視在台灣地區銷售之典型利率變動型壽險之公平定價問題。假設資產過程滿足Heston隨機變動模型、利率過程為CIR 模型，保險給付將為一系列遠期起點期權之總和。本文就台灣財務市場之資料進行模型參數估計，再利用蒙地卡羅法計算契約公平價格，同時計算風險值（VaR, ES）。本文第三章闡述國際板債券評價系統的實作細節。台灣保險業總資產近兩成之國際板債券在IFRS-9 會計準則下非為純債務工具，必須以公允價值衡量。在此我們敘述以美國固定期限公債收益率或美元LIBOR及ICE利率交換率校正的利率期限結構，配合芝加哥期貨交易所的歐式利率交換選擇權隱含波動度資料估計Hull-White 短期利率模型之評價理論細節，並使用開放原始碼程式語言Python 與函式庫QuantLib 及三元樹演算法實作國際板債券評價系統。除與櫃買中心系統價格輸出結果相比較外，我們展示本系統在給定利率期限結構與市場現有商品規格下可贖回債券期初價值與隱含年利率、不可贖回期間與可贖回頻率關係之計算。本文第四章探討copula-GARCH 模型在變額年金保證價值計算上的應用。有效的風險管理前提在於推估各種資產間的機率關係，並計算反映系統狀態的各種定量指標的能力。現代計算技術的進步使得更符合實際、不須過份簡化的多變量機率模型運用變為可能，而copula 正是如此的多變量機率模型。結合GARCH 時間序列模型，我們利用一系列基於無母數統計與經驗過程理論的穩健統計檢定方法，針對給定S&P500 與S&P600 指數時間序列選擇並匹配最適copula-GARCH 模型，進而推估變額年金保證價值。
