17Financial Theory

17Financial Theory - Financial Theory...

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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?
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