'''

==== Deterministic Short Rate

Interest rates in general and short rates in particular are not constant over time. You rather observe something called a term structur of insterest rates in financial markets. Simply speaking, this means that a ZCB maturing at latexmath:[$s \geq 0$] will have a different yield than another bond of the same type maturing at latexmath:[$t \geq s$]. _Yield_ in this case is defined as the quantity latexmath:[$y_t$] that solves the equation latexmath:[$D_0(t)=e^{-y_t t}$] for a ZCB maturing at latexmath:[$t$]. Analogously, yield is also the quantity latexmath:[$y_s$] that solves the equation latexmath:[$D_0(s)=e^{-y_s s}$] for a ZCB maturing at latexmath:[$s$].'''

from constant_short_rate import *

class deterministic_short_rate(object):

''' Class for discounting based on deterministic short rates,

derived from a term structure of unit Zero-Coupon Bond yields

Attributes

==========

name : string

name of the object

yield_list : list/array of (time, yield) tuples

input yields with time attached

Methods

=======

get_interpolated_yields :

return interpolated yield curve given a time list/array

get_forward_rates :

return forward rates given a time list/array

get_discount_factors :

return discount factors given a time list/array

'''

def __init__(self, name, yield_list):

self.name = name

self.yield_list = np.array(yield_list)

if np.sum(np.where(self.yield_list[:, 1] < 0, 1, 0)) > 0:

raise ValueError, 'Negative yield(s).'

def get_interpolated_yields(self, time_list, dtobjects=True):

''' time_list either list of datetime objects or list of

year deltas as decimal number (dtobjects=False)

'''

if dtobjects is True:

tlist = get_year_deltas(time_list)

else:

tlist = time_list

dlist = get_year_deltas(self.yield_list[:, 0])

if len(time_list) <= 3:

k = 1

else:

k = 3

yield_spline = sci.splrep(dlist, self.yield_list[:, 1], k=k)

yield_curve = sci.splev(tlist, yield_spline, der=0)

yield_deriv = sci.splev(tlist, yield_spline, der=1)

return np.array([time_list, yield_curve, yield_deriv]).T

def get_forward_rates(self, time_list, dtobjects=True):

yield_curve = self.get_interpolated_yields(time_list, dtobjects)

if dtobjects is True:

tlist = get_year_deltas(time_list)

else:

tlist = time_list

forward_rate = yield_curve[:, 1] + yield_curve[:, 2] * tlist

return np.array((time_list, forward_rate)).T

def get_discount_factors(self, time_list, dtobjects=True):

discount_factors = []

if dtobjects is True:

dlist = get_year_deltas(time_list)

else:

dlist = time_list

forward_rate = self.get_forward_rates(time_list, dtobjects)

for no in range(len(dlist)):

factor = 0.0

for d in range(no, len(dlist) - 1):

factor += ((dlist[d + 1] - dlist[d])

* (0.5 * (forward_rate[d + 1, 1] + forward_rate[d, 1])))

discount_factors.append(np.exp(-factor))

return np.array((time_list, discount_factors)).T