近年來因市場波動劇烈, 保險公司紛紛推出的「附保證投資型保單」, 給 予保戶在投資上的保證。然而, 附最低給付保證條件卻使得保險公司必須面 對更大的核保與財務風險。所以計算出附有最低保證條件商品的保費就顯 得格外地重要。 傳統附保證保單在訂價時,都是假設固定己知的脫退率,因為他們認為 脫退率的變化不會是影響保單價值的主因。但在Mary hardy 所著的《Investment Guarantees》一書中page 96 特別提到脫退風險: Withdrawals are more problematic. Withdrawals are, to some extent, related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. 因此, 本文希望透過建立受經濟因子影響的解約率模型,來得到附保證保險 的風險價差。 本文考慮附保證滿期給付投資型商品(GMMB),並且使用 Heston (1993) 提出的財務市場模型以及參考Mercurio (1996,2001) 評價投資型保險之風 險承擔價差方法, 使用效用函數來描述保險契約雙方之風險趨避程度。同 時根據Kolkiewicz & Tan (2006) 假設受經濟因子的危險比率模型(hazard rate model), 來反映出資產的平均波動程度會影響保戶的脫退率。最後以 情境方式分別模擬5、10及15年到期的附保證最低滿期投資型保險之風險 價差。本研究推導之模型主要得出下列結果: (1) 保單期間愈長, 價差愈大。 (2) 價外賣權的價差高於價內。(3) 風險規避程度越高買賣價差越大。(4) 脫 退率受經濟影響愈深, 保單的買賣價差愈大。(5) 當保險公司所保證的價格 愈高時, 價差的影響愈大。 / With the fluctuation in the financial market in 2008, insurance company provided the consumers with equity-linked life insurances embedded guarantees. On the other hand, there are more risk in the financial literacy and underwriting performance of the insurance company. It is especially important to calculate the premium of the contract embedded investment guarantee properly . Traditional method of pricing the contract embedded investment guarantee was assumed that lapse rate was known, because product providers believed lapse rate was not a major factor to price the contract. However, Mary hardy’s ”Investment Guarantees” page 96 specifically mentions about the lapse rate risk: Withdrawls are more problematic. Withdrawals are, to some extent ,related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. So this article will found the model of lapse rate dependent on economic factors and further get the fair value of one kind of a contract embedded guarantee: GMMB. We will build a financial model introduced by Heston (1993) and use the methodology provided by Mercurio (1996,2001) to price the risk bearing gap of a contract embedded guarantee with utility function to depict the risk averse level between investors . And we have lapse rates affected from the fluctuation of the implying asset which is the hazard rate model used by Kolkiewicz & Tan (2006). Finally, we will simulate a set of scenarios to present the Risk bearing spreads of equity-linked life insurance embedded guarantees whose term are 5、10 and 15 years. The following are the consequences I got: (1) The longer the duration, the larger the spread. (2) The spread out of money is larger than that in the money. (3) The higher the risk aversion, the larger the buy-ask spread. (4) The deeper the influence of economy on the lapse rate, the larger the buy-ask spread. (5) The higher guarantee price insurer offer, the deeper the spread affect.

本文建立了當違約機率及回收率為隨機變動，同時信用等級移動有記憶性，且回收率和無風險利率期間結構相關之信用風險價差期間結構模型。並評價信用價差選擇權及有對手違約風險普通選擇權之價值。 此模型產生的信用價差有更多的變化性，將可描述：信用價差的隨機波動行為，且即使信用等級沒變，價差仍可能發生改變；信用價差與無風險利率期間結構有相關性；公司特定或證券特定的價差及其變動行為；處於等級上升或下降趨勢公司債券之殖利率曲線，能更準確配適有風險債券的價格等實際現象。 並可應用至有對手違約風險之商品及多種信用衍生性商品等的評價與避險，且可進行風險管理方面的應用。 關鍵詞：信用風險；信用風險價差；馬可夫模型；信用衍生性商品 / In this thesis we develop a credit migration model with memory for the term structure of credit risk spreads. Our model incorporates stochastic default probability, stochastic recovery rate, and the correlation between the recovery rate and the term structure of risk-free interest rates. We derive valuation formulae for a credit spread option and a plain vanilla option with counterparty risk. This model provides greater variability in credit spreads, and it has properties in line with what have been observed in practice: (1) credit spreads show diffusion-like behavior even though the credit rating of the firm has not changed; (2) the model injects correlation between spreads and the term structure of interest rates; (3) the model enables firm-specific and security-specific variability of spreads to be accommodated; and (4) the model enables us to estimate the yield curves corresponding to the positive and negative trends of credit ratings and match the observed risky bond prices more precisely. This model is useful for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging credit derivatives, and for risk management. Key Words: Credit Risk, Credit Risk Spread, Markov Model, Credit Derivative.