In all the pricing, with all the products considered so far, it has been assumed that all obligations will be met, in full and without delay. It has been assumed that bonds will pay their coupons, in full, on coupon dates. Shares would pay out their dividends as required. The holders of forward contracts and futures contracts, swaps and options will all pay up what they owe on the day payment is due. But what if we remove this assumption? What if we admit the possibility of default, of firms going into bankruptcy or administration and being unable to meet their financial obligations? These things certainly happen in the real world. Bankruptcies and defaulted payments might be comparatively rare events, but when they do occur, their effects can be dramatic. Setting up procedures to cope with events such as these is a major activity in the financial world. In this chapter, we offer a glimpse of the problems forming the subject matter of one of the most exciting recent developments in financial mathematics. We will consider two problems.

1. (1) How can we measure the likelihood (probability) of a company experiencing some form of financial difficulty?

2. (2) What measures can a company take to protect itself against the event that an organisation which owes it money falls into financial difficulties?