Final Exam
FIN 525 FixedIncome Securities
Philip H. Dybvig
Washington University in Saint Louis
March, 2005
This is a closedbook examination. Answer all questions as
directed. Mark your answers directly on the examination. There
are no trick questions on the exam. There are some formulas
from the course (including some you will not need) at the end
of the exam. All cash flows and interest rates are annual.
Good luck!
A. General Concepts Short Anwer: 20 points (Answer
each question in no more than two sentences of ordinary
length.)

When interest rates rise, what happens to most bond prices?

If the spot interest rate rises 1% today, do we expect the 10year
forward rate to rise by more than 1%, by less than 1%, or by 1%?

What is the usual reason to buy an interest cap?

Does a coupon bond's duration rise, fall, or stay the same when
interest rates rise? Explain.

Is mortgage fallout higher or lower when rates rise? Explain why.
B. Basic rates and arbitrage 30 points
Today we can buy or sell a
riskless claim paying $100 a year from now for $75. Or, we can
buy a selfamortizing claim paying $100 one year out and $100 two
years out for $140.

What are the discount factors for one year
out and two years out?

What are the implied one and twoyear par coupon yields?

Suppose you
can buy or sell a twoperiod par coupon bond yielding 30%.
Construct an arb with the original two claims.
C. Duration 20 points
A pension liability consists of three cash flows: $625 million 5
years out, $800 million 10 years out, and $250 million 15 years out.
The liability is funded by a single asset, a pure discount bond maturing
in 10 years. The market value of the pension asset equals the market
value of the liability, that is, the pension is fully funded in economic
terms.

The discount factor is 0.8 for 5 years out, 0.5 for 10 years out, and
0.4 for 15 years out. What is the market value of the liability?

What is the duration of the liability? What is the duration of the
asset?

According to the duration measure, will the reduction in market value
be larger for the asset or for the liability if rates rise? Explain
briefly.
D. Binomial Option Pricing 30 points
Assume that the interest rate starts at 4% and in each period
and either increases by 2% or decreases by 2% (from 4% up to 6% or
down to 2% would be the first move). The riskneutral probabilities
of ups and downs are all 1/2.

What is the price now of a discount bond with face of $100
maturing one year from now?

What is the price now of a discount bond with face of $100
maturing two years from now?

What is the price today of a twoyear collar with a cap
price of 5% and a floor price of 3%? The underlying
notional is $1,000.