論文名稱：可轉換公司債存續期間之分析 校所組別：國立政治大學金融研究所 畢業時間：九十年度第二學期 提要別：碩士學位論文提要 研究生：陳嘉霖 指導教授：陳松男博士 論文提要及內容： 本研究在分析可轉債的存續期間，在存續期間的衡量上是採用有效存續期間法；而在可轉換公司債的評價上，假設股票價格服從幾何布朗寧運動，無風險利率的變動符合Hu1I-white利率模型，並且考量利率與股票報酬之間的相關性，建立可轉換公司債評價六元樹形圖。 本研究分別針對到期期限長短、價內外程度、股價波動度、利率波動度、股價與利率相關係數及票面利率等六項參數，作可轉換公司債存續期間的敏感度分析，研究結果為：1 加入贖回條款後，可轉債的存續期間高於未加任何條款下的可轉債存續期間。2 加入賣回條款後，可轉債的存續期間低於未加任何條款下的可轉債存續期間。3 加入贖回及賣回候款後，可轉債的存續期間會介於僅含贖回條款與僅含賣回條款的存續期間之中。4 距到期日愈長可轉債的存續期間愈高。5 愈價外的可轉債其存續期間愈高。6 股票波動度愈高，可轉債的存續期間愈低。7 利率波動度增加則可轉債的存續期間上升。8 股票價格與利率相關係數由正至負，可轉債的存續期間上升。9 若贖回權愈小，則票息上升會增加可轉債的存續期間。 關鍵字：可轉換公司債、存續期間、有效存續期間、六元樹、Hull-white、利率模型 / Title of Thesis: Anatomy of the Convertible Bond Duration Name of Institute: Graduate Institute of Money and Banking, NCCU Graduate Date: June, 2002 Name of Student: Chen, Chia-Lin Advisor: Dr. Chen, Son-Nan Abstract: This thesis uses effective duration method to anatomize the convertible bond duration. With the assumptions that stock price follows Geometric Brownian Motion and risk-free interest rate follows Hull and White model, we built a hexanomial tree to value the convertible bond. This thesis analyses the effects of the six parameters . They are maturity date, the ratio of the stock price versus the strike price, the correlation between stock return and interest rate, stock return volatility, interest rate volatility, and coupons. The conclusions include nine points. First, the value of convertible bond duration including call clauses is higher then pure convertible bond duration. Second, the value of convertible bond duration including put clauses is lower than pure convertible bond duration. Third, the value of convertible bond duration including both call and put clauses is between only including call or put clauses ones. Fourth, the longer the time to maturity is, the higher the convertible bond duration is. Fifth, the higher the ratio of the strike price versus the stock price is , the higher the convertible bond duration is. Sixth, the higher the stock volatility is , the lower the convertible bond duration is. Seventh, the higher the interest rate volatility is , the higher the convertible bond duration is. Eighth, the value of the correlation between stock return and interest rate increases from a negative value to a positive one, then the convertible bond duration increases. Ninth, if the value of call right is very small , the convertible bond duration will increase by the increasing of the coupon . Keywords: Convertible Bond, Duration, Effective Duration, Hexanomial Tree, Hull and White Interest Rate Model

本研究的第一部份是利用有效存續期間與有效凸性來衡量人壽保險人的利率風險。我們發現Tsai (2009)指出的壽險保單準備金之有效存續期間結構並非一般化的結果。當長期利率水準高於保單預定利率及保單解約率敏感於利差時，準備金之有效存續期間會呈現與Tsai (2009)相反的結構。我們進一步發現準備金之有效凸性會亦有可能呈現負值，且不易依照保單到期期限歸納出一般化的結構。負值的有效凸性起因於準備金並非利率的單調函數，且準備金與利率的函數關係隨保單到期期限而不同。我們的研究結果可以幫助人壽保險人執行更為精確的資產負債管理。 本研究的第二部分是利用模擬最佳化的方法，幫助銷售傳統壽險保單的保險人求解出適切的業務槓桿與資產配置策略。我們假設保險人在考量破產機率與報酬率的波動之下，將資本與淨保費收入投資於資本市場中，以追求較高的業主權益報酬率。以業務槓桿與資產配置相互影響為前提，我們求解出適切的業務槓桿與多期資產配置策略，並分析在不同的業務槓桿之下，保險人多期資產配置的差異。 / In the first part of this doctoral dissertation, we focus on a proper measurement on interest rate risk of life insurer’s liabilities, policy reserves, by incorporating the general effective duration and effective convexity measures. Tsai (2009) identified a term structure of the effective durations of life insurance reserves. We find that his results are not general. When the long-run mean of interest rates is higher than the policy crediting rate and the surrender rate is sensitive to the spread, the term structure would exhibit an opposite pattern to the one in Tsai (2009). We further find that the effective convexities might be negative and the term structure of the effective convexities exhibits no general pattern. The irregularities originate from negative effective convexities result from the relationship between mean reserves and initial short rate for different years to maturity. Our results can help life insurers to implement more accurate asset-liability management. In the second part, we analyze asset allocation and leverage strategies for a life insurer selling traditional insurance products by using a simulation optimization method. We assume that an insurer invests equity capital (from its shareholders) and premiums it receives from policyholders by choosing a portfolio intended to maximize the annual return of equity minus the penalty of insolvencies and risks. We regard the leverage as an internal factor in asset allocation. Based on these assumptions, we get a promising multiple-periods asset allocation and leverage, besides analyzing how leverage affects asset allocation strategies.