! 10.11.f90
! 2024-10-09
! $Id: 10.11.f90 1.1 2024/11/03 07:23:57 s Exp $
!
! a : amount
! d : discount factor, d[k] = d(0,k)
! f : forward rate, f[k] = f(k-1,k) 
! g(r) : pv2 - pv1
! pv1 : present value in variable rate
! pv2 : present value in fixed rate
! r : fixed rate
! s : spot rate, s[k] = s(k)
! x : cash flow in variable rate, x[0] = x(k)
! y : cash flow in fixed rate, y = a * r

program b
implicit none
integer :: i,n
real(8) a, d(6), f(6),pv1, r,root,s(6), x(6), y

! input
s = [0.070d0, 0.073d0, 0.077d0, 0.081d0, 0.084d0, 0.088d0]
f = [0.0,   0.0,   0.0,   0.0,   0.0,   0.0]
a = 1000d0
n = 6

! calculation
do i = 1, n
    if(i == 1) then
        f(1) = s(1)
    else
        f(i) = (1.0 + s(i)) ** i / (1.0 + s(i - 1)) ** (i - 1) - 1d0
    end if
end do
x = a * f(1:n)
do i = 1, n
    d(i) = 1d0 / (1d0 + s(i)) ** i 
end do
pv1 = sum(x(1:n) * d(1:n))

! solve g(r)=0
do i = 8700, 8900
    r = i / 1d5
    if( g(a,r,pv1) > 0) then
        root=r
        exit
    end if
end do

! output
print *, '10.10.py'
print '(a7,f8.2)',   'a', a
print '(a7,7f8.3)',  's', (s(i), i = 1, n)
print '(a7,7f8.3)',  'f', (f(i), i = 1, n)
print '(a7,7f8.3)',  'x', (x(i), i = 1, n)
print '(a7,7f8.3)',  'd', (d(i), i = 1, n)
print *, 'pv1 in variable rates ', pv1
print *, 'r, g(r)', root, g(a,root,pv1)
stop

contains
! function
real(8) function g(a,r,pv1) ! g=pv2-pv1
    implicit none
    real(8) a,d1,d2,d3,d4,d5,d6,pv1,pv2,r
    d1 = 1 / (1d0 + r) ** 1
    d2 = 1 / (1d0 + r) ** 2
    d3 = 1 / (1d0 + r) ** 3
    d4 = 1 / (1d0 + r) ** 4
    d5 = 1 / (1d0 + r) ** 5
    d6 = 1 / (1d0 + r) ** 6
    y   = a * r
    pv2 = y * (d1 + d2 + d3 + d4 + d5 + d6)
    g   = pv2 - pv1
end function g
end program b