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LOS 35.g: Describe path-wise valuation in a binomial
interest rate framework and calculate the value of a fixed- READING 35: THE ARBITRAGE-FREE VALUATION FRAMEWORK
income instrument given its cash flows along each path.
MODULE 35.2: BINOMIAL TREES, PART 2
The path-wise valuation approach mathematically identical to
the backward induction method. Given a BIRT with n (say n =3)
2
periods, there are 2 (n–1) (say 2 (3-1 ) = 2 = 4) unique paths
comprising one known spot rate (S) and varying combinations of
two unknown upper (U) and lower (L) forward rates outcomes in
our binomial framework: SUU, SUL, SLU, and SLL.
EXAMPLE: How will you use path-wise valuation to
value the same $100 par option-free 3-year, 3 percent
treasury bond?
Same prior results = $94.485!
Answer: It’s an n = 3 years bond; so number of unique
paths = 2 (n–1 = 2
2 = 4
