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Default Curve
1 Introduction
Starting from coupon bonds, we were able to deduce the prices of zero coupon bonds
and the forward rates in a world without default. The forward curves enabled us to
see what traders think future interest rates will be, assuming they believe there is
no uncertainty in the world (because in that case the forward interest rates will be
exactly the same as they think future interest rates will be). Since government bond
traders spend a lot of time thinking about what future interest rates will be, they are
likely to be better informed about this than the general public. The public can infer
their opinions from the forward rates, without having to do the work of forecasting
the future.
We shall now introduce the simplest possible kind of uncertainty. We shall suppose
that in every period, either all the bonds in a country (say Argentina) deliver fully or
else they all default completely forever after. We shall then derive the "implied default
probabilities" each year. By seeing the implied default probability curve the general
public can deduce what the traders think the probability of default is in any year,
assuming that they the traders care only about the expected number of dollars they
make. You may not know whether things are getting worse or better in Argentina.
But by looking at Argentine bond prices, you can deduce what wellinformed traders
think.
Putting the same thing di
f
erently, if you believe that you have a very reliable
estimate of the probability of default in Chile (say because you keep up with your
Yale classmate who is now their minister of
f
nance), and if your estimate di
f
ers from
what the market thinks, then you can bet on the di
f
erence and make risky arbitrage
pro
f
ts. If you think the chances are 5% and the market thinks they are 10%, then
you will be able to buy the bonds at a price that on average gives you a higher than
the riskless rate of return (American interest rate). Of course if the bond defaults
you will lose a lot of money.
Finding the default probabilities sounds complicated, but in fact it is a very simple
perturbation of what we did to
f
nd the yield curve in the last chapter.
One fairly recent new security is called a credit derivative. It pays $1 if an Ar
gentine bond defaults on a particular date, or at any time before a particular date.
To price such a security is straightforward, once you have the default probabilities.
To
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 '09
 GEANAKOPLOS,JOHN
 Interest Rates

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