"Lec 16 - Backward Induction and Optimal Stopping Times" Financial Theory (ECON 251) 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. 00:00 - Chapter 1. Calculating Default Probabilities 14:58 - Chapter 2. Relationship Between Defaults and Forward Rates 28:09 - Chapter 3. Zermelo, Chess, and Backward Induction 36:48 - Chapter 4. Optimal Stopping Games and Backward Induction 01:06:47 - Chapter 5. The Optimal Marriage Problem Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Fall 2009.
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Lec 2- Utilities, Endowments, and Equilibrium
Lec 4- Efficiency, Assets, and Time
Lec 5- Present Value Prices and the Real Rate of Interest
Lec 6 - Irving Fisher's Impatience Theory of Interest
Lec 7 - Shakespeare's Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance
Lec 8 - How a Long-Lived Institution Figures an Annual Budget. Yield
Lec 10 - Dynamic Present Value
Lec 12 - Overlapping Generations Models of the Economy
Lec 13 - Demography and Asset Pricing: Will the Stock Market Decline when the Baby Boomers Retire?
Lec 14 - Quantifying Uncertainty and Risk
Lec 15 - Uncertainty and the Rational Expectations Hypothesis
Lec 17 - Callable Bonds and the Mortgage Prepayment Option
Lec 18 - Modeling Mortgage Prepayments and Valuing Mortgages
Lec 19 - History of the Mortgage Market: A Personal Narrative
Lec 21 - Dynamic Hedging and Average Life
Lec 22 - Risk Aversion and the Capital Asset Pricing Theorem
Lec 23 - The Mutual Fund Theorem and Covariance Pricing Theorems
Lec 24 - Risk, Return, and Social Security
Lec 25 - The Leverage Cycle and the Subprime Mortgage Crisis