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.

According to the rational expectations hypothesis, traders know the probabilities of future events, and value uncertain future payoffs by discounting their expected value at the riskless rate of interest. Under this hypothesis the best predictor of a firm’s valuation in the future is its stock price today. In one famous test of this hypothesis, it was found that detailed weather forecasts could not be used to improve on contemporaneous orange prices as a predictor of future orange prices, but that orange prices could improve contemporaneous weather forecasts.

In this lecture, we use the overlapping generations model from the previous class to see, mathematically, how demographic changes can influence interest rates and asset prices. We evaluate Tobin’s statement that a perpetually growing population could solve the Social Security problem, and resolve, in a surprising way, a classical argument about the link between birth rates and the level of the stock market. Lastly, we finish by laying some of the philosophical and statistical groundwork for dealing with uncertainty.

This lecture continues the analysis of Social Security started at the end of the last class. We describe the creation of the system in 1938 by Franklin Roosevelt and Frances Perkins and its current financial troubles. For many Democrats, Social Security is the most successful government program ever devised and for many Republicans Social Security is a bankrupt program that needs to be privatized. Is there any way to reconcile the views of Democrats and Republicans? How did the system get into so much financial trouble?

Where can you find the market rates of interest (or equivalently the zero coupon bond prices) for every maturity? This lecture shows how to infer them from the prices of Treasury bonds of every maturity, first using the method of replication, and again using the principle of duality. Treasury bond prices, or at least Treasury bond yields, are published every day in major newspapers. From the zero coupon bond prices one can immediately infer the forward interest rates.