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 = 9
rrate = make_spot_table(r0, u, d, n_years)
print('Spot rate grid=')
print(round(upper_triangular_to_ascending_triangle(rrate), 3)) ## print in the format of this chapter 

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

q = 0.5


## Part (a):
##
V = 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] 
        if( jj == n_steps ){ ## this is t=T-1
            V[ii, jj] = 106 / R + 6                                   ## at t=T we get the face value plus the only coupon then we discount till t=T-1 and get another coupon
        }else if( jj == 1 ){ ## this is t=1
            V[ii, jj] = ( q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1] )/R     ## at t=1 we dont get a coupon payment
        }else{
            V[ii, jj] = ( q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1] )/R + 6 ## for other time points you get the bond plus the coupon 
        }
    }
}
colnames(V) = paste0('t_', seq(0, n_years))
V_print = upper_triangular_to_ascending_triangle(V) ## print in the format of this chapter
print(round(V_print, 2))


## Part (b):
##
V = 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] 
        if( jj == n_steps ){ ## this is t=T-1
            pv = 106 / R + 6                                          ## at t=T we get the face value plus the only coupon then we discount till t=T-1 and get another coupon
            call_value = 100 + 6                                      ## OR we get the face value plus the due coupon 
            V[ii, jj] = min(pv, call_value)
        }else if( jj == 1 ){ ## this is t=1
            V[ii, jj] = ( q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1] )/R     ## at t=1 we dont get a coupon payment
        }else{
            pv = ( q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1] )/R + 6        ## for other time points you get the bond plus the coupon
            call_value = 100 + 6                                      ## OR we get the face value plus the due coupon 
            if( jj-1 < 5 ){
                V[ii, jj] = pv                                        ## the bond is not callable yet 
            }else{
                V[ii, jj] = min(pv, call_value)
            }
        }
    }
}
colnames(V) = paste0('t_', seq(0, n_years))
V_print = upper_triangular_to_ascending_triangle(V) ## print in the format of this chapter
print(round(V_print, 2))