source('http://waxworksmath.com/Authors/A_F/Conte/Code/Chapter3/utils.R')
##source('../../../../Conte/Code/Chapter3/utils.R')

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

r0 = 0.07
u = 1.3
d = 0.9

## Part (a):
##

## 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, 3))

N = 10 ## the notional dollar amount
Payments = N * rrate ## these are the payments that must be made at the end of each year 
print('Payments= ')
print(round(Payments, 3))

## Price the SWAP:
##
V = 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) ){
        r = rrate[ii, jj]
        if( jj==(n_years+1) ){
            V[ii, jj] = Payments[ii, jj] / ( 1 + r )
        }else{

            V[ii, jj] = ( Payments[ii, jj] + 0.5 * V[ii, jj+1] + 0.5 * V[ii-1, jj+1] ) / ( 1 + r )
        }
    }
}
colnames(V) = paste0('t_', seq(0, n_years))
print('SWAP Value=')
print(round(V, 3))


## There are two ways of working this problem:
##

## 1) Using the Fixed rate == Variable rate equation
##
rrate = make_spot_table(r0, u, d, n_years+1)
rrate = upper_triangular_to_ascending_triangle(rrate)
print('Short rate grid (one extra year)=')
print(round(rrate, 3))

## Compute the elementary prices from the short rates: 
##
E0 = short_rate_lattice_to_elementary_prices(rrate)
print(round(E0, 3))

## Sum the columns of the elementary price grid:
##
E0[is.na(E0)] = 0
E00 = colSums(E0)
E00 = E00[-1]
print(E00)

r = V[n_years+1, 1] / ( N * sum(E00) )
print(sprintf('Fixed rate SWAP==Variable rate SWAP: r= %f', r))


## 2) Using the Fixed rate == Variable rate equation
##

## 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, 3))


fixed_rate_r_to_swap_value = function(rfixed, rrate){
    ##
    ## For a fixed interest rate for payment evaluate a swap value
    ##
    n_years = dim(rrate)[1]-1

    Payment = N * rfixed ## these are the fixed rate payments that must be made at the end of each year 

    ## Price the SWAP with these payments: 
    ##
    V = 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) ){
            r = rrate[ii, jj]
            if( jj==(n_years+1) ){
                V[ii, jj] = Payment / ( 1 + r )
            }else{
                V[ii, jj] = ( Payment + 0.5 * V[ii, jj+1] + 0.5 * V[ii-1, jj+1] ) / ( 1 + r )
            }
        }
    }
    ##V[n_years+1, 1] ## return the initial price
    V ## return the full grid
}
##
## Test this function:
##print(fixed_rate_r_to_swap_value(0.08, rrate))
##

rt = bisection_method(0.05, 0.1, function(x) {V=fixed_rate_r_to_swap_value(x, rrate); V[dim(V)[1], 1] - 3.9790})
print(sprintf('Build fixed rate payment lattice: r= %f', rt[1]))


## For Exercise 9 we need both grids:
##
V_floating = V
V_fixed = fixed_rate_r_to_swap_value(rt[1], rrate)

print('V_floating=')
print(round(V_floating, 3))
print('V_fixed=')
print(round(V_fixed, 3))