In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.