  In this paper we continue the research of our recent interest rate tree model
called Zero Black-Derman-Toy (ZBDT) model, which includes the possibility of a
jump at each step to a practically zero interest rate. This approach allows to
better match to risk of financial slowdown caused by catastrophic events. We
present how to valuate a wide range of financial derivatives for such a model.
The classical Black-Derman-Toy (BDT) model and novel ZBDT model are described
and analogies in their calibration methodology are established. Finally two
cases of applications of the novel ZBDT model are introduced. The first of them
is the hypothetical case of an S-shape term structure and decreasing volatility
of yields. The second case is an application of the ZBDT model in the structure
of United States sovereign bonds in the current $2020$ economic slowdown caused
by the Coronavirus pandemic. The objective of this study is to understand the
differences presented by the valuation in both models for different
derivatives.
