Game Pricing For Permanent Convertible Bonds Based On TF Model

Permanent convertible bonds are a type of convertible bonds with no maturity. Thevalue of the bonds is time independence and only related to the price of the underlyingassets. In any time, the issuer can call the bonds by a previously agreed price and the holdercan convert the bonds into a previously agreed proportion of stocks.In this paper we consider the stcok of company as the underlying assets and assumethat the stock price is driven by a double exponential downward jump-diffusion processwhen default occurs. Within the Tsiveriotis-Fernands(the following TF for short) modelframework, we develop a differential-integral equations pricing model by-hedging methodas used in the Ayache-Forsyth-Vetzal(the following AFV for short) model and then raise afree boundary problem according to call and conversion features. On this basis, we consierthe valuation of permanent convertible bonds. By solving a system of differential-integralequations, we give the pricing formula under different call and conversion conditions. Basedon game pricing theory, by direct comparison, we also prove that this solution is the gamefair price when the issuer and holder executive the optimal stopping strategies in the game.