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

## Part (b):
##
r0 = 0.1
u = 1.2
d = 0.9

## Get the grid of possible short rates:
##
n_years = 4
rrate = make_spot_table(r0, u, d, n_years)
print('Spot rates=')
print(round(rrate, 4))

p_default = 0.1
p_no_default = 1 - p_default

## Solve for the_value of the bond that might default: 
##
n_steps = n_years+1 ## = number of columns = number of years + the initial spot_value
n_rows = n_steps

B = matrix(NA, nrow=n_rows, ncol=n_steps)
for( jj in seq(n_rows, 1, -1) ){
    for( ii in 1:jj ){
        R = 1 + rrate[ii, jj] ## the total discount rate        
        if( jj == n_steps ){ ## the final column/timestep
            B[ii, jj] = ( p_no_default * 110 + p_default * 0 ) / R
        }else{
            B[ii, jj] = ( p_no_default * ( 0.5 * B[ii, jj+1] + 0.5 * B[ii+1, jj+1] + 10 ) )/R
        }
    }
}
## Give this table descriptive column names:
##
colnames(B) = paste0('t_', seq(0, n_years))
print(round(B, 6))