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.

1. Why Finance?
2. Utilities, Endowments, and Equilibrium
3. Computing Equilibrium
4. Efficiency, Assets, and Time
5. Present Value Prices and the Real Rate of Interest
6. Irving Fisher's Impatience Theory of Interest
7. Shakespeare's Merchant of Venice, Collateral. Present Value and the Vocabulary of Finance
8. How a Long-Lived Institution Figures an Annual Budget. Yield
9. Yield Curve Arbitrage
10. Dynamic Present Value
11. Social Security
12. Overlapping Generations Models of the Economy
13. Demography and Asset Pricing: Will the Stock Market Decline when the Baby Boomers Retire?
14. Quantifying Uncertainty and Risk
15. Uncertainty and the Rational Expectations Hypothesis
16. Backward Induction and Optimal Stopping Times
17. Callable Bonds and the Mortgage Prepayment Option
18. Modeling Mortgage Prepayments and Valuing Mortgages
19. History of the Mortgage Market: A Personal Narrative
20. Dynamic Hedging
21. Dynamic Hedging and Average Life
22. Risk Aversion and the Capital Asset Pricing Theorem
23. The Mutual Fund Theorem and Covariance Pricing Theorems
24. Risk, Return, and Social Security
25. The Leverage Cycle and the Subprime Mortgage Crisis
26. The Leverage Cycle and Crashes

This course attempts to explain the role and the importance of the financial system in the global economy. Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.

Course Structure:
This Yale College course, taught on campus twice per week for 75 minutes, was recorded for Open Yale Courses in Fall 2009.