An investor who plans to invest at a later time might be curious to know what the future interest rate might look like, as implied by today's term structure of interest rates. For example, you might ask: What is the one-year spot rate one year from now? To answer this question, one can calculate forward rates for the period between 
and 
using this formula:
Here, 
and 
are the continuously compounded annual interest rates at time period and respectively.
The following Python code helps us generate a list of forward rates from a list of spot rates:
"""
Get a list of forward rates
starting from the second time period
"""
class ForwardRates(object):
def __init__(self):
self.forward_rates = []
self.spot_rates = dict()
def add_spot_rate(self, T, spot_rate):
self.spot_rates[T] = spot_rate
def __calculate_forward_rate___(self, T1, T2):
R1 = self.spot_rates[T1]
R2 = self.spot_rates[T2]
forward_rate = (R2*T2 - R1*T1)/(T2 - T1)
return forward_rate
def get_forward_rates(self):
periods = sorted(self.spot_rates.keys())
for T2, T1 in zip(periods, periods[1:]):
forward_rate =
self.__calculate_forward_rate___(T1, T2)
self.forward_rates.append(forward_rate)
return self.forward_ratesUsing spot rates derived from our preceding yield curve, we get the following result:
>>> fr = ForwardRates() >>> fr.add_spot_rate(0.25, 10.127) >>> fr.add_spot_rate(0.50, 10.469) >>> fr.add_spot_rate(1.00, 10.536) >>> fr.add_spot_rate(1.50, 10.681) >>> fr.add_spot_rate(2.00, 10.808) >>> print fr.get_forward_rates() [10.810999999999998, 10.603, 10.971, 11.189]
Calling the get_forward_rates method of the ForwardRates class returns a list of forward rates, starting from the next time period.