在風險中立測度下，分析可轉換債的提前與延遲贖回現象以及與其他實證研究做比較

Abstract

可轉換公司債是一種同時具有債權和股權性質很普及的公司債，許多學者利用賽局理論來分析可轉換公司債－持有人的轉換策略以及發行公司的贖回策略之間的相互作用。在考慮稅盾和破產成本下，本文以立體樹狀模型來分析可轉換公司債，為了修正用樹狀模型所產生的離散誤差和數值誤差，本篇利用二分法和Bino-trinomial tree (BTT) 來調整贖回邊界的準確性，並且分析最大化股東權益、最小化可轉換公司債價值和完美市場決策三種贖回策略；發現最大化股東權益贖回策略顯著的比最小化可轉換公司債價值容易產生延遲贖回現象或減輕提前贖回現象，而我們利用完美市場決策來判斷前二者策略是否發提前或延遲贖回現象，除了上述三種策略，模型中的經濟變數也會影響延遲(提前)贖回現象產生，在本篇模型中發現：利率下降顯著地產生提前贖回現象，債息、提前贖回價值和稅率上升會顯著地產生延遲贖回現象。最後把研究結果和其他實證研究做比較，並且試著解釋這些現象產生的原因。

A convertible bond is a popular type of corporate bond that has hybrid attributes of both bonds and equities. The interactions between the conversion strategies owned by bond investors and call strategies owned by issuers can be modeled by game theory analyses. By taking the impacts of tax benefits and bankruptcy costs, this thesis numerically evaluates convertible bonds with a 3D tree model. To adjust the oscillations of call boundary caused by the discretization errors and the numerical errors of the tree model, I use the BTT model and the bisection method to improve the accuracy of boundary analyses. Three types of call strategies, the maximizing equity value policy、the minimizing debt value policy and perfect market rule, are analyzed; I observe that the first policy causes more significant delay call phenomenon than the second one. The impacts of other economic variables on early/delay call phenomenon are also analyzed in my numerical model. I find that the decrement of the interest rate level will result in more significant early call phenomenon; and the increment of the early redemption value and the tax rate will result in more significant delay call phenomenon. I compare my results with past empirical studies and try to give insights for these phenomena.