source('../Chapter3/utils.R')
source('../Chapter12/utils.R')
source('../Chapter14/utils.R')

r0 = 0.07
u = 1.3
d = 0.9

## Get the grid of short rates:
##
n_years = 5
rrate = make_spot_table(r0, u, d, n_years)
print('Short rate grid=')
rrate = upper_triangular_to_ascending_triangle(rrate)
print(round(rrate, 4))

## Get the "Payment rate" lattice (the left lattice in Figure 14.8):
##
Payments = matrix(NA, nrow=(n_years+1), ncol=(n_years+1))
for( jj in seq(n_years+1, 1, -1) ){
    n = (n_years+1 - jj) ## number of years
    for( ii in (2+n_years-jj):(n_years+1) ){
        if( jj==(n_years+1) ){
            Payments[ii, jj] = 100
        }else{
            r = rrate[ii, jj] + 0.02 ## 2% over the short rate 
            Payments[ii, jj] = annuity_payment(100, n, r)
        }
    }
}
colnames(Payments) = paste0('t_', seq(0, n_years))
print('Payments Rate Lattice=')
print(round(Payments, 2))

## Get the "Value grid":
##
Value = matrix(NA, nrow=(n_years+1), ncol=(n_years+1))
for( jj in seq(n_years+1, 1, -1) ){
    for( ii in (2+n_years-jj):(n_years+1) ){
        if( jj==(n_years+1) ){
            Value[ii, jj] = 0
        }else if( jj==n_years ){
            r = rrate[ii, jj] + 0.02 ## 2% over the short rate
            R = 1 + r 
            Value[ii, jj] = 100 * R / ( 1 + rrate[ii, jj] ) - 100 
        }else{
	    YP = Payments[ii, jj] ## what payment would the bank receive at the end of the year 
            r = rrate[ii, jj] + 0.02 ## 2% over the short rate
	    Interest_Part = 100 * r
	    New_Loan_Value = 100 - YP + Interest_Part
	    numer = New_Loan_Value * ( 1 + (0.5 * Value[ii-1, jj+1] + 0.5 * Value[ii, jj+1])/100 ) + YP
	    denom = 1 + rrate[ii, jj]
            Value[ii, jj] = numer / denom - 100 
        }
    }
}
colnames(Value) = paste0('t_', seq(0, n_years))
print('Value Per 100 Lattice=')
print(round(Value, 3))