def Curvature(self, t_value):
''':param t_value: A time value
:type t_value: a positive integer, float or decimal
:return: The curvature in a nelson Siegel curve at time t_value
'''
weight = t_value * self.scale
if weight:
return (self.curvature *
((1 - _exp(-weight)) / weight - _exp(-weight)))
else:
return 0
def discount_factor(self, t_value):
''':param t_value: A time value
:type t_value: a positive integer, float or decimal
:return: The discount factor at time t_value
'''
if t_value >= 0:
return _exp(-self.continous_forward_rate(t_value) * t_value)
else:
return 0
def Slope(self, t_value):
''':param t_value: A time value
:type t_value: a positive integer, float or decimal
:return: The Slope in a nelson Siegel curve at time t_value
'''
weight = t_value * self.scale
if weight:
return self.slope * (1 - _exp(-weight)) / weight
else:
return self.slope
def discrete_forward_rate(self, t1_value, t2_value):
''':param t1_value: A time value
:type t1_value: a positive integer, float or decimal,
t1_value < t2_value
:param t2_value: A time value
:type t2_value: a positive integer, float or decimal,
t1_value < t2_value
:return: The discrete forward rate between time t1_value and t2_value
'''
rate1 = self.continous_forward_rate(t1_value)
rate2 = self.continous_forward_rate(t2_value)
average_rate = ((t2_value * rate2 - t1_value * rate1) /
(t2_value - t1_value))
return _exp(average_rate) - 1
def zero_coupon_rate(self, t_value):
''':param t_value: A time value
:type t_value: a positive integer, float or decimal
:return: The zero coupon rate at time t_value
'''
return _exp(self.continous_forward_rate(t_value)) - 1