# One year defaultible bond with 40% recovery, 8% coupon semiannualy and risk free rate of 5%. Face value is 100.
# The bond yield is 6.5% l1 is the first year hazard rate
from math import *
r = 0.05
l1 = 0.0246
y = 0.065
# Cash flow from recovery rate if default happens at .25, .75 time point ( mid point between coupon payments )
x1 = exp(-r*0.25)*(1 - exp(-l1*0.5))
x2 = exp(-r*0.75)*( exp(-l1*0.5) - exp(-l1))
# Cash flow from coupon if default does not happen
y1 = exp(-l1*0.5 - r * 0.5)
y2 = exp(-l1 - r )
print(40*(x1 + x2) + 4 * y1 + 104 * y2)
print(4 * exp(-y * 0.5) + 104 * exp(-y * 1))
# Two year defaultible bond with 40% recovery, 8% coupon semiannualy and risk free rate of 5%. Face value is 100.
# The bond yield is 6.8% l1 is the first year hazard rate and l2 is the second year hazard rate
from math import *
r = 0.05
l1 = 0.0246
l2 = 0.0348
y = 0.068
# Cash flow from recovery rate if default happens at .25, .75, 1.25, 1.75 time point ( mid point between coupon payments )
x1 = exp(-r*0.25)*(1 - exp(-l1*0.5))
x2 = exp(-r*0.75)*( exp(-l1*0.5) - exp(-l1))
x3 = exp(-r*1.25)*( exp(-l1) - exp(-l1 - .5*l2))
x4 = exp(-r*1.75)*( exp(-l1 - .5*l2)- exp(-l1-l2))
# Cash flow from coupon if default does not happen
y1 = exp(-l1*0.5 - r * 0.5)
y2 = exp(-l1 - r )
y3 = exp(-l1 - 0.5 * l2 - r * 1.5 )
y4 = exp(-l1 - l2 - r * 2 )
print(40*(x1 + x2 + x3 + x4) + 4 * (y1 + y2 + y3 ) + 104 * y4)
print(4 * ( exp(-y * 0.5) + exp(-y * 1) + exp(-y * 1.5) ) + 104 * exp(-y * 2) )