可轉換公司債是同時兼具權益與負債特質的混合證券，是ㄧ個複雜而又被廣泛運用的金融商品，可轉債持有者可以在未來特定時間將債券轉換為普通股股票，亦可以賣回給公司或是公司主動買回，因此可轉換公司債的評價又牽涉到不同信用風險的問題。在Kostas Tsiveriotis, Chris Fernandes (1998) 將可轉債分割成現金部位和股權部位，考慮不同部位須承受不同程度的風險，再利用聯立偏微分方程組來評價可轉換公司債。但台灣可轉換公司債通常訂有重設條款令方程式的求解產生路徑相依的問題，因此無法使用傳統的有限差分法來求解，因此引入Longstaff and Schwartz (2001)所提出的最小平方蒙地卡羅法來解決路徑相依的問題，利用此種新的數值方法，我們可以考慮重設條款及凍結期間等可轉債發行條件。在我們選出的16支可轉換公司債作的實證結果顯示，在發行時，可轉換公司債的理論價格高出市場價格18.93%。

　　Convertible bond is a hybrid security consisting of a straight bond and a call on the underlying equity. Credit risk plays an important role for valuing convertible bond. Kostas Tsiveriotis, Chris Fernandes (1998) provided a split pricing model that can be accurate valuing the equity and fixed-income part with different credit risk simultaneously. But, the issuing provision in Taiwan often including reset provision causes path dependent problem that is not easy to solve for traditional finite difference method. Longstaff and Schwartz (2001) provide a new numerical method which is called least square Monte Carlo method to solve path dependent problem. In the empirical result, we find the theoretical issuing price is higher than market price on average for 18.93%.

Ammann, M., A. Kind, C. Wilde. Are convertible bonds underpriced? An analysis of the French market. Journal of Banking & Finance, 27, 2003, 635-653.
Andersen, L., and D. Buffum. Calibration and Implementation of Convertible Bond Modes. Working paper, Banc of America Securities, 2003.
Ayache, E., P. A. Forsyth, and K.R. Vetzal. Valuation of Convertible Bonds with Credit Risk. The Journal of Derivatives Fall 2003,9-29
Ayache, E., K.R. Verzal, and P.A Forsyth. Next Generation Models for Convertible Bond with Credit Risk. Wilmott Magazine, December 2002, pp. 68-77
Ayache, E., The Discrete and the Continuous. Working Paper, ITO 33, S.A, 2001.
Arzac, E.R., PERCS, DECS, and Other Mandatory Convertibles. Journal of Applied Corporate Finance, 10 (1997), pp. 54-63.
Becker, J., A Second Order Backward Difference Method with Variable Time Steps for a Parabolic Problem. BIT 38(1998), pp. 644-662
Beneish, M.D., and E. PRESS. Interrelation Among Events of Default. Contemporary Accounting Research, 12(1995), pp. 57-84
Brennan M.J., E.S. Schwartz. Analyzing Convertible Bonds. The Journal of Financial and Quantitative,1980,Vol.15,No.4,907-929.
Brennan, M.J., and E.S. Schwartz. Analyzing Convertible Bonds. Journal of Financial and Quantitative Analysis, 15(1980), pp. 907-929.
Black, F., and J.C. Cox. Valuing Corporate Securities: Some Effects of Bond Indenture Provisions. Journal of Finance, 31(1976), pp. 351-367
Cooper, J., and M. Martin. Default Risk and Derivative Products. Applied Mathematical Finance 3 (1996), pp. 53-74.

Cheung, W., and I. Nelken. Costing the Converts. Risk, 7(July 1994), pp. 47-49
Clark, T.A., and M.I. Weinstein. The Behavior of the Common Stock of Bankrupt Firms. Journal of Finance, 38(1983), pp. 489-504
Davis, M., and F.R. Lischka. Convertible Bonds with Market Risk and Credit Risk. Working Paper, Tokyo-Mitsubishi International, 1999.
Duffe, D., and K.J. Singleton. Modeling Term Structures of Defaultable Bonds. Review of Financial Studies, 12(1999). Pp.687-720
Forsyth, P.A., and K.R. Vetzal. Implicit Solution of Uncertain Volatility/Transaction Cost Option Pricing Models with Discretely Observed Barriers. Applied Numerical Mathematics,36 (2001), pp. 2096-2123
Hull, J., Options, Futures and Other Derivatives, 5th ed. Upper Saddle River, NJ: Prentice-Hall,2003
Hung, M.-W., and J.-Y. Wang Pricing Convertible Bonds Subject to Default Risk. The Journal of Derivatives, 10(Winter 2002), pp. 75-87
Hillion, P., and T. Vermaelen. Death Spiral Convertibles. Working paper, INSEAD, 2001
Ho, T.S.Y., and D.M Pfeffer. Convertible Bonds: Model, Value Attribution, and Analytics.Financial Analysts Journal, 52(September/October 1996), pp. 35-44
Hull, J., A. White. Valuing Derivative Security Using Explicit Finite Difference Method. Journal of Financial and Quantitative Analysis, Vol. 25, No.1 (Mar 1990), 87-100
Ingersoll J.E. A Contingent-Claims Valuation of Convertible Securities. Journal of Financial Economics, 1977, 4, 289-322.
Ingersoll, J., Jr. A Contingent-Claims Valuation of Convertible Securities. Journal of Financial Economics, 4(1997) pp.289-322
Jarrow R.A., D. Lando, S.M.Turnbull. A Markov Model for the Term Structure of Credit Risk Spreads. The Review of Financial studies, 1997, Vol. 10, No. 2, 481-523.
Jarrow, R.A., and S.M. Turnbull. Pricing Derivative Securities on Financial Securities Subject to Credit Risk. Journal of Finance, 50 (1995), pp. 53-85
Longstaff, F.A., E.S. Schwartz. Valuing American option by simulation: A simple least-squares approach. The Review of Financial Studies Spring 2001 Vol. 14, No. 1, pp. 113-147
Longstaff, F.A., and E.S. Schwartz. A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance, 50 (1995), pp. 789-819
Madan, D., and H. Unal. A Two-Factor Hazard Rate Model For Pricing Risky Debt and the Term Structure of Credit Spreads. Journal of Financial and Quantitative Analysis, 35(2000), pp.43-65
Muromachi, Y. The Growing Recognition of Credit Risk in Corporate and Financial Bond Markets. Working Paper 126,NLI Research Institude,1999.
Mcconnell J.J., E.S. Schwartz. LYON Taming. The Journal of finance,Vol.41, No.3, 1985, 561-576.
Merton R.C. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. The Journal of Finance, 1973,Vol.29, No.2,449-470.
Nyborg, K.G. The Use and Pricing of Convertible Bonds. Applied Mathematical Finance, 3(1996), pp. 167-190.
Rannacher, R. Finite Element Solution of Diffusion Problems with Irregular Data. Numerische Mathmatik, 43 (1984), pp.309-327.
Schultz, A. In These Convertibles, A Smoother Route to Stocks. The New York Times, April 7, 2002.
Takahashi, A., T. Kobayashi, and N. Nakagawa. Pricing Convertible Bonds With Default Risk. The Journal of Fixed Income, 11 (December 2001), pp. 20-29.
Takahashi, A.T.K., N. Nakagawa. Pricing convertible bonds with default risk. The Journal of Fixed Income ,2001.
Tsiveriotis, K., C. Fernandes. Valuing Convertible Bonds with Credit Risk. The Journal of Fixed Income,1998.
Yigitbasioglu, A.B. Pricing Convertible Bonds with Interest Rate, Equity, Credit and FX Risk. Discussion Paper 2001-14, ISMA Center, University of Reading, 2001. Available.
Zvan, R., P.A. Forsyth, and K.R. Verzal. A Finite Volume Approach To Contingent Claims Valuation. IMA Journal of Numerical Analysis, pp. 703-731.