In this lecture, Professor Donald Kagan offers a sketch of the Greek heroic code of ethics. He shows that in this community, arête (manly virtue) and honor are extremely important and even worth dying for, as the case of Achilles makes clear. In addition, Professor Kagan shows how this society eventually produced a new phenomenon, the rise of the polis. The discussion ends with a strong emphasis on the importance of the polis in Greek history.

In this lecture, Professor Kagan addresses what scholars call the Homeric question. He asks: what society do Homer's poems describe? He argues that in view of the long oral transmission of the poems, the poems of Homer probably reflect various ages from the Mycenaean world to the Dark Ages. More importantly, close scrutiny of the poems will yield historical information for the historian. In this way, one is able to reconstruct through the poems, to a certain extent, the post-Mycenaean world. Finally, Professor Kagan says a few words on the heroic ethic of the Greek world.

In this lecture, Professor Donald Kagan explores the earliest history of Greek civilization. He demonstrates how small agricultural enclaves eventually turned into great cities of power and wealth in the Bronze Age, taking as his examples first Minoan Crete and then Mycenaean Greece. He also argues that these civilizations were closely related to the great monarchies of the ancient Near East. He points out that the Mycenaean age eventually came to an abrupt end probably through a process of warfare and migration.

Professor Donald Kagan explains why people should study the ancient Greeks. He argues that the Greeks are worthy of our study not only because of their vast achievements and contributions to Western civilization (such as in the fields of science, law, and politics) but also because they offer a unique perspective on humanity. To the Greeks, man was both simultaneously capable of the greatest achievements and the worst crimes; he was both great and important, but also mortal and fallible. He was a tragic figure, powerful but limited.

Until now we have ignored risk aversion. The Bernoulli brothers were the first to suggest a tractable way of representing risk aversion. They pointed out that an explanation of the St. Petersburg paradox might be that people care about expected utility instead of expected income, where utility is some concave function, such as the logarithm. One of the most famous and important models in financial economics is the Capital Asset Pricing Model, which can be derived from the hypothesis that every agent has a (different) quadratic utility.

This lecture reviews the intuition from the previous class, where the idea of dynamic hedging was introduced. We learn why the crucial idea of dynamic hedging is marking to market: even when there are millions of possible scenarios that could come to pass over time, by hedging a little bit each step of the way, the number of possibilities becomes much more manageable. We conclude the discussion of hedging by introducing a measure for the average life of a bond, and show how traders use this to figure out the appropriate hedge against interest rate movements.

Suppose you have a perfect model of contingent mortgage prepayments, like the one built in the previous lecture. You are willing to bet on your prepayment forecasts, but not on which way interest rates will move. Hedging lets you mitigate the extra risk, so that you only have to rely on being right about what you know. The trouble with hedging is that there are so many things that can happen over the 30-year life of a mortgage. Even if interest rates can do only two things each year, in 30 years there are over a billion interest rate scenarios.

Professor Geanakoplos explains how, as a mathematical economist, he became interested in the practical world of mortgage securities, and how he became the Head of Fixed Income Securities at Kidder Peabody, and then one of six founding partners of Ellington Capital Management. During that time Kidder Peabody became the biggest issuer of collateralized mortgage obligations, and Ellington became the biggest mortgage hedge fund.

A mortgage involves making a promise, backing it with collateral, and defining a way to dissolve the promise at prearranged terms in case you want to end it by prepaying. The option to prepay, the refinancing option, makes the mortgage much more complicated than a coupon bond, and therefore something that a hedge fund could make money trading. In this lecture we discuss how to build and calibrate a model to forecast prepayments in order to value mortgages. Old fashioned economists still make non-contingent forecasts, like the recent predictions that unemployment would peak at 8%.

This lecture is about optimal exercise strategies for callable bonds, which are bonds bundled with an option that allows the borrower to pay back the loan early, if she chooses. Using backward induction, we calculate the borrower's optimal strategy and the value of the option. As with the simple examples in the previous lecture, the option value turns out to be very large. The most important callable bond is the fixed rate amortizing mortgage; calling a mortgage means prepaying your remaining balance.