Pricing Option With Credit Risk In Lévy Process

With the development of financial market, a lot of new methods are implement-ed to price these derivatives. E.g. martingale method. Martingale is a very usefulmathematical tool in option pricing. It solves a lot of problems which is difficult forpartial differential equations to solve and it makes the option pricing easier. Esschertransform is a very effective martingale method to find the equivalent martingale mea-sure. Esscher transform was first introduced by Gerber and Shiu. They use Esschertransform to price the ordinary option. We extend one-dimensional Esscher transformto multi-dimensional Esscher transform, and use multi-dimensional Esscher transformto price the vulnerable option.In this paper, the research object is a special class of options - vulnerable option,the option with default risk. We discuss its nature and the pricing problem driven bydifferent Levy process. Esscher transform is used in this paper to price the vulnerableoption. We find the equivalent martingale measure to price the option. We also discussthe options driven by different Levy process. The article also focused on a special formof vulnerable option, covered options. As the vulnerable option involves two assets,we use two-dimensional Esscher transform to price the vulnerable option.