Page 35 - FINAL CFA II SLIDES JUNE 2019 DAY 9
P. 35
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 = the one-
period forward rate for that period
3
2
(say, (1 + S ) = (1 + S ) (1 + F2) as
2
3
implied from the benchmark spot rate
curve (forward rate pricing model).
