Arbitrage Pricing of Convertible Securities with Credit Risk

In this paper, we attempt to shed more light on the mathematical modeling of convertible bonds. Towards this end we shall study generic defaultable game options and defaultable convertible securities, which encompass defaultable convertible bonds (and also more standard defaultable American or European options) as special cases. Moreover, we shall examine these contracts in the framework of a fairly general market model in which prices of primary assets are assumed to follow semimartingales (see Delbaen and Schachermayer (1997) or Kallsen and Kuhn (2005)) and the random moment of default is exogenously given