Financial Theory: Lecture 17 Transcript
November 3, 2009
<< back
Professor John Geanakoplos:
I think I'll try to start. So last time we found out how to evaluate options,
especially stopping options where you don't have so many options. You either do something or you don't do
it. That's the simplest kind of option.
And we discovered through two examples, at least, that the option is worth more than people realize. So this
time we're going to apply that--and that the way to figure out exactly what it's worth and exactly what to do is
to work by backward induction.
So this time we're going to apply that reasoning to the two most important options in the economy, one is
callable bonds and a much more important one is the mortgage option. And all of you at some time in your
lives will probably own houses and have a mortgage option and have to think about what kind of mortgage to
get and what the option is. So I want to teach you how to think about that problem.
So let's start with the callable bond problem. Uh-oh, I forgot to turn this on. So let's start here with the
callable bond problem. So callable bonds are issued by corporations and they pay, usually, an interest rate,
say 9 percent. So the bond pays 9 percent, 9 percent and then some years later it pays 109, but at any point in
time you have the option, the company has the option of calling the bond, and calling it for--so it's going to
pay 9 + 100 at the end, so here it's 9. So at any time the company has the option of calling the bond. So what
does that mean?
It means after it's paid the 9--the company's issued a bond promising to pay 9 for say 10 years and then the
principal in the 10th year, this is year 10, the total of 109. So that's the simplest possible bond. And the
company occasionally has the option, we'll see in a minute why it would want this option, has the option of
saying, "Okay, we don't want to make the rest of those payments. We want to get out of our promise. We've
just paid you 9. We'll pay off the extra 100 that we're eventually going have to owe and we'll call it a day." So
this is the payment and this is the remaining balance. So for a callable bond the remaining balance is always
100.
So it's pretty obvious that if you've made an arrangement, so I owe you--like for example the prototypical
mortgage was exactly of this kind. Somebody borrows money from you and they say, "I promise to pay you 9
dollars a year until the last year when I'm going to pay you 109. This is called, for those old mortgages it was
called the balloon payment, but in typical bonds it's just the principal payment, the 100 face value of the
bond.
So the person who borrowed the money and has agreed to pay off over the years, he might have a reason why
the house he put up as collateral is no longer going to be his house. He might want to move in which case the
lender doesn't have a house anymore backing the loan and they have to have some way of resolving the loan
and ending it. So the question is, after you've made a payment, how can you resolve the rest of the loan which
is supposed to go on for 6 more years?