Valuing Convertible Bonds With Credit Risk And Risk Management

There are two parts in the dissertation.Part one: Based on the analysis of the basic pricing models of Convertible Bonds,Tsiveriotis-Fernands (the following TF for short)Model, we give the theoretical deriva-tion of the TF Model and take credit risk into consideration as in the Ayache-Forsyth-Vetzal(the following AFV for short) Model to improve the TF model and get a newpricing model for Convertible Bonds. There is numerical analysis through which wecan see the solution of the new pricing model is very similar to the solution of the AFVModel,thus we can prove the rationality of the theoretical derivation of the TF Modelwhich separates the Convertible Bond into two parts.Part two: On the base of TF Model, we research the Greek Letters which includeDelta and Gamma to manage the risks.Because the convertible bonds can be exercised before the expiration date, thevalue of the convertible bonds satisfy Variational Inequality. To get the solution ofthe Greek Letters, we can use the Penalty Function to make the Inequality becomeEquality and manage the risks. From the result, we know that this method is verygood for calculating Delta but it is bad for Gamma because of the δ function.