May 2012
Beginner
441 pages
11h 44m
English
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The Bootstrap Method
It is convenient to be able to determine a set of discount rates for zero coupon bonds from current coupon bonds. Recall, for example, the immunization problem of the previous chapter for which the liability had duration 10 years but there were no matching zero coupon bonds available to hold against that liability. Bootstrapping is a method that extracts discount rates for zero coupon bonds using observed prices on existing coupon bonds. I will demonstrate the method and follow it with an application.
Assume all bonds have a face value M of $100. The following table lists some hypothetical bond information on maturity, coupon, and price.
Bootstrap Table A.
We will use continuous discounting, which means that the continuously discounted rate rc is determined as before, that is, as
Taking natural logarithms extracts the continuously compounded rate of return, viz.,
The first bond is a 90-day maturity zero coupon bond that returns $1.5 on the $98.5 price for a discrete annual return of 4∗$1.5/$98.5 = 6.09 percent. Converting to continuous time, this rate is 4∗ln(1 + .0609/4) = 6.04 percent. We do likewise for the six-month and the one-year bonds, which have discrete ...
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