MMA708 – Analytical Finance II –Jan R. M. Röman. BLACK-DERMON-TOY MODEL WITH FORWARD INDUCTION. Wei Wang Maierdan Halifu Yankai Shao. INTRODUCTION. Black-Derman-Toy model (a short rate model) is a model of the evolution of the yield curve.
Key features of BDT-model
Volatilities Curve - array of yield volatilities for the same bonds.
As input, both two curves come form the term structure.
The short rate is given by the following process:
the factor in front of ln(r) is the speed of mean reversion (gravity)
θ(t) divided by the speed of mean reversion is a time-dependent mean-reversionlevel.
The price tree and its corresponding rate tree
A One-Step Tree
from Future Prices
We first derive prices 1 step in the future from
prices 2 steps in the
future with the same
When we move further to a four-step tree, we must remember that the Black-Derman-Toy model is built on the following assumptions:
4-period rate tree as inputs to solve 5-period price tree
Results: Rate Tree
Results: Bond Tree