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LOS 35.e: Describe the process of calibrating a READING 35: THE ARBITRAGE-FREE VALUATION FRAMEWORK
binomial interest rate tree to match a specific
term structure.
MODULE 35.1: BINOMIAL TREES, PART 1
In practice, the interest rate tree is usually generated using specialized computer
software, conforming to 3 rules: Calibration Rule 1: Generate
arbitrage-free values, that is, the
value of bonds must = their market
price, which excludes arbitrage
opportunities, otherwise it will fail to
properly price more complex callable
and putable securities, which is its
intended purpose!
Calibration Rule 2: Adjacent forward
rates (for the same period) are two
2σ
standard deviations apart (e ) away.
This allows us to use one forward rate
to for a particular nodal period to
compute the other forward rates for
that period in the tree.
Calibration Rule 3: The middle
forward rate (or mid-point in case of
even number of rates) in a period is
approximately equal to the implied
(from the benchmark spot rate curve)
one-period forward rate for that period
(say F3 for S2).
