Provisions Analysis And Pricing Study Of Convertible Bonds

The convertible bond is a kind of mid-long-term mixed financial tool which is between the bond and the stock. It endows some rights to the invester to continue holding the bond till the expiry date or to convert the bond to the stock before the expiry date. In this paper, our purpose is to analyse some special provisions and study the pricing problem of convertible bonds.The first part is the base of this paper. Secondly, we discuss one of the distinguished provisions of the convertible bond, the convertibility which brings to the problem of the optimal stopping time. Carrying out several theorems and their proofs under the continuous time background, we work out the rational exercise policy on the basis of Martingale theory. Thirdly, we study another distinguished provision, the strategy of calling and converting. We use the strategy theory to analyse a two-person non-co-operative game structure for the convertible bond and then solve the Nash equilibrium points with the economic sense. Fourthly, we stick to the pricing and the optimal convert boundary under the one-factor model. Applying the fundamental solution in the differential equation, we discuss the American free boundary of the convertible bond and probe into the optimal convert boundary and the pricing analysis. Fifthly, we introduce a two-factor models under the suppose of random rate and moreover, we add the credit risk to the random rate two-factor model by introducing the instantaneous risk of default. Furthermore, we study the pricing problem with the callable and puttable provisions. We obtain the weak formulation that is helpful to the numerical computation.