Pricing and Hedging of Defaultable Models

In the world of finance, it is crucial to consider the models based on the fact that the companies may default. Hearing the word ¿default¿ one can imagine the biggest defaults in the history of economy like that of Lehman Brothers in 2008. However, the exact definition of a default explains it only as a failure to meet debt obligations such as loans or bonds. The debtor is in default when he is either unable or unwilling to pay the debt. One has to distinguish the default from a state of being unable to pay the debts precisely which is called insolvency. The company is insolvent when it is unable to pay debts as they fall due (cash flow insolvency) or when the liabilities exceed the assets (balance sheet insolvency). It is worth mentioning that the insolvency can lead to a bankruptcy which is the process of legally defining a financial situation as insolvent. While modelling credit risk, one usually takes under consideration the company¿s default in general, without looking into the causes and hence distinguishing between being unable or unwilling to pay the debts.