Chapter 2: FAQs 179
What is Bootstrapping Using Discount
Factors?
Short Answer
Bootstrapping means building up a forward interest-
rate curve that is consistent with the market prices of
common fixed-income instruments such as bonds and
swaps. The resulting curve can then be used to value
other instruments, such as bonds that are not traded.
Example
You know the market prices of bonds with one, two
three, five years to maturity. You are asked to value a
four-year bond. How can you use the traded prices so
that your four-year bond price is consistent?
Long Answer
Imagine that you live in a world where interest rates
change in a completely deterministic way, no random-
ness at all. Interest rates may be low now, but rising
in the future, for example. The spot interest rate is the
interest you receive from one instant to the next. In this
deterministic interest-rate world this spot rate can be
written as a function of time,r(t). If you knew what this
function was you would be able to value fixed-coupon
bonds of all maturities by using the discount factor
exp
(
−
∫T
t
r(τ)dτ
)
,
to present value a payment at timeTto today,t.
Unfortunately you are not told what thisrfunction is.
Instead you only know, by looking at market prices of
various fixed-income instruments, some constraints on
thisrfunction.
