1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
import numpy as np
from ctypes import *
from quantlib.time.schedule import Schedule, CDS
from quantlib.time.api import Actual360, Period, UnitedStates, Following, today
from quantlib.util.converter import qldate_to_pydate, pydate_to_qldate
import pandas as pd
from scipy.special import h_roots
from common import root
import os
libloss = np.ctypeslib.load_library("lossdistrib", os.path.join(root, "code/R/lossdistrib/src"))
libloss.fitprob.restype = None
libloss.fitprob.argtypes = [
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),
POINTER(c_int),
POINTER(c_double),
POINTER(c_double),
np.ctypeslib.ndpointer('double', ndim=1, flags='F,writeable')]
libloss.stochasticrecov.restype = None
libloss.stochasticrecov.argtypes = [
POINTER(c_double),
POINTER(c_double),
np.ctypeslib.ndpointer('double', ndim=2, flags='F'),
np.ctypeslib.ndpointer('double', ndim=2, flags='F'),
POINTER(c_int),
POINTER(c_double),
POINTER(c_double),
POINTER(c_double),
np.ctypeslib.ndpointer('double', ndim=1, flags='F,writeable')]
libloss.BCloss_recov_dist.restype = None
libloss.BCloss_recov_dist.argtypes = [
np.ctypeslib.ndpointer('double', ndim=2, flags='F'),# defaultprob
POINTER(c_int),# nrow(defaultprob)
POINTER(c_int),# ncol(defaultprob)
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),# issuerweights
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),# recovery
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),# Z
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),# w
POINTER(c_int), # len(Z) = len(w)
np.ctypeslib.ndpointer('double', ndim=1, flags='F'), # rho
POINTER(c_int), # Ngrid
POINTER(c_int), #defaultflag
np.ctypeslib.ndpointer('double', ndim=2, flags='F,writeable'),# output L
np.ctypeslib.ndpointer('double', ndim=2, flags='F,writeable')# output R
]
libgq = np.ctypeslib.load_library("GHquad", os.path.join(root, "code", "python"))
libgq.GHquad.restype = None
libgq.GHquad.argtypes = [c_int,
np.ctypeslib.ndpointer('double', ndim=1, flags='F'),
np.ctypeslib.ndpointer('double', ndim=1, flags='F')]
def GHquad(n):
Z, w = h_roots(n)
return Z*np.sqrt(2), w/np.sqrt(np.pi)
def stochasticrecov(R, Rtilde, Z, w, rho, porig, pmod):
q = np.zeros_like(Z)
libloss.stochasticrecov(byref(c_double(R)), byref(c_double(Rtilde)), Z, w, byref(c_int(Z.size)),
byref(c_double(rho)), byref(c_double(porig)), byref(c_double(pmod)), q)
return q
def fitprob(Z, w, rho, p0):
result = np.empty_like(Z)
libloss.fitprob(Z, w, byref(c_int(Z.size)), byref(c_double(rho)), byref(c_double(p0)), result)
return result
def BCloss_recov_dist(defaultprob, issuerweights, recov, rho, Z, w, Ngrid = 101, defaultflag = False):
L = np.zeros((Ngrid, defaultprob.shape[1]), order='F')
R = np.zeros_like(L)
rho = np.repeat(rho, issuerweights.size)
libloss.BCloss_recov_dist(defaultprob, byref(c_int(defaultprob.shape[0])),
byref(c_int(defaultprob.shape[1])),
issuerweights, recov, Z, w, byref(c_int(Z.size)), rho,
byref(c_int(Ngrid)), byref(c_int(defaultflag)), L, R)
return L, R
def adjust_attachments(K, losstodate, factor):
"""
computes the attachments adjusted for losses
on current notional
"""
return np.minimum(np.maximum((K-losstodate)/factor, 0), 1)
def trancheloss(L, K1, K2):
return np.maximum(L - K1, 0) - np.maximum(L - K2, 0)
def trancherecov(R, K1, K2):
return np.maximum(R - 1 + K2, 0) - np.maximum(R - 1 + K1, 0)
def tranche_cl(L, R, cs, K1, K2, scaled = False):
if(K1 == K2):
return 0
else:
support = np.linspace(0, 1, L.shape[0])
size = K2 - K1 - np.dot(trancheloss(support, K1, K2), L) - \
np.dot(trancherecov(support, K1, K2), R)
sizeadj = 0.5 * (size + np.hstack((K2-K1, size[:-1])))
if scaled:
return 1/(K2-K1) * np.dot(sizeadj * cs["coupons"], cs["df"])
else:
return np.dot(sizeadj * cs["coupons"], cs["df"])
def tranche_pl(L, cs, K1, K2, scaled=False):
if(K1 == K2):
return 0
else:
support = np.linspace(0, 1, L.shape[0])
cf = K2 - K1 - np.dot(trancheloss(support, K1, K2), L)
cf = np.hstack((K2-K1, cf))
if scaled:
return 1/(K2-K1) * np.dot(np.diff(cf), cs["df"])
else:
return np.dot(np.diff(cf), cs["df"])
def tranche_pv(L, R, cs, K1, K2):
return tranche_pl(L, cs, K1, K2) + tranche_cl(L, R, cs, K2, K2)
def creditSchedule(tradedate, tenor, coupon, yc, enddate = None):
tradedate = pydate_to_qldate(tradedate)
start = tradedate - Period('4Mo')
enddate = pydate_to_qldate(enddate)
if enddate is None:
enddate = tradedate + Period(tenor)
cal = UnitedStates()
DC = Actual360()
sched = Schedule(start, enddate, Period('3Mo'), cal, date_generation_rule=CDS)
prevpaydate = sched.previous_date(tradedate)
sched = [d for d in sched if d>=prevpaydate]
df = [yc.discount(d) for d in sched if d > tradedate]
dates = pd.to_datetime([str(d) for d in sched if d > tradedate], "%m/%d/%Y")
coupons = np.diff([DC.year_fraction(prevpaydate, d) * coupon for d in sched])
return pd.DataFrame({"df":df, "coupons":coupons}, dates)
def cdsAccrued(tradedate, coupon):
tradedate = pydate_to_qldate(tradedate)
start = tradedate - Period('3Mo')
end = tradedate + Period('3Mo')
start_protection = tradedate + 1
DC = Actual360()
cal = UnitedStates()
sched = Schedule(start, end, Period('3Mo'), cal, date_generation_rule=CDS)
prevpaydate = sched.previous_date(tradedate)
return DC.year_fraction(prevpaydate, start_protection) * coupon
|
