Page 34 - PowerPoint Presentation

LOS 35.c: Describe a binomial interest rate READING 35: THE ARBITRAGE-FREE VALUATION FRAMEWORK
tree framework (BIRT).
Assumes rates have an equal probability of taking one of two value the MODULE 35.1: BINOMIAL TREES, PART 1
next period. Over multiple periods, the set of possible interest rate paths
used to value bonds is called a binomial interest rate tree.

Adjacent is e 2σ Away: i 1,U = i e 2σ or i 1,L = i 1,U e- 2σ
1,L
= i 2,LL e 4σ = i 3,LLL e 8σ
where:
e ≈ 2.7183 (base of natural log)
σ = standard deviation (volatility)
of interest rates
The relationship
among the set of
rates (branches)
associated with
each individual
i 2,UL = = i 2, LL e 2σ nodal period
(stem) is a
function of the
interest rate
(roots) volatility
assumed to
generate the tree.
e = BIRT Framework is a lognormal random walk
model with 2 desirable properties:
(1) higher volatility at higher rates; and
(2) non-negative interest rates.

σ = estimated from historical data or implied from Implications? For exams, you might only need 1 to solve the rest
interest rate derivatives.