source('../Chapter12/utils.R')
source('../Chapter14/utils.R')

r0 = 0.06
u = 1.2
d = 0.9

## Get the grid of spot rates:
##
n_years = 10
rrate = make_spot_table(r0, u, d, n_years)
rrate = upper_triangular_to_ascending_triangle(rrate)
print('Short rate lattice=')
print(round(rrate, 3))

E0 = short_rate_lattice_to_elementary_prices(rrate)
print(round(E0, 3))

## Sum the columns of the elemntary price grid:
##
E0[is.na(E0)] = 0
E00 = colSums(E0)
print('Bond prices=')
print(E00)

ks = 0:(n_years+1)
sk = (1/E00)^(1/ks) - 1
sk_pct = sk * 100 
print('Forward rates=')
print(round(sk_pct, 2))