Bootstrapping theoretical spot rate curve

Reference book:
1. Fabozzi - Bond Markets, Analysis and Strategies
2. CFA - Level I Fixed Income Kaplan Notes Book 5

There are two types of bootstrapping:

1. From par yield curve [ref 1]
2. From bond price [ref 2]

The following is an example of bootstrapping from bond price:

Bootstrap the following bond prices to derive the discount factors, and forward rates for each 6-month period (s/a basis).

(BEY - Bond equivalent yield)


99.86=(100+3/2)/(1+BEY0_5/2)
BEY0_5=0.03284598
# discount factor
DF0_5 =1/(1+BEY0_5) = 0.9681986


101.43=2.5/(1+BEY0_5/2) + 102.5/(1+BEY1_0/2)^2
BEY1_0=0.03535077
# forward rate [ref 1]
(1+BEY1_0/2)^2=(1+BEY0_5/2)(1+F05_1/2) =>
F05_1=((1+BEY1_0/2)^2/(1+BEY0_5/2)-1)*2 = 0.0378586463
# discount factor
DF1_0 =1/(1+BEY1_0/2)^2=0.9655649

100.31=2/(1+BEY0_5/2) + 2/(1+BEY1_0/2)^2 + 102/(1+BEY1_1/2)^3
BEY1_1=...