The main aim of this work is to price defaultable bonds. In order to achieve this goal we link first hitting densities of Brownian motion with functionals of controlled diffusions. From a practical point of view examples of diffusions with this property are: Brownian motion with linear drift,...

A credit default swap (CDS) is a financial contract in which the holder of the instrument will be compensated in the event of a loan default. When available, CDS's are used to monitor the credit risk of countries and companies. In this work we develop a closed form procedure to value a CDS in...

A barrier option is a financial derivative which includes an activation (or deactivation) clause within a standard vanilla option. For instance, a copper mining company could secure to sell in at least K dollars each ton of copper during the next year, by buying M European put options. However,...