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from .basket_index import BasketIndex
from .db import _engine
from .tranche_functions import (
credit_schedule, adjust_attachments, cds_accrued, GHquad, BCloss_recov_dist,
BCloss_recov_trunc, tranche_cl, tranche_pl)
from .index_data import get_singlenames_curves, get_tranche_quotes
from copy import deepcopy
from pyisda.cdsone import upfront_charge
from pandas.tseries.offsets import BDay
from scipy.optimize import brentq
from scipy.interpolate import CubicSpline, PchipInterpolator
from scipy.special import logit, expit
import concurrent.futures
import pandas as pd
import numpy as np
class TrancheBasket(BasketIndex):
def __init__(self, index_type: str, series: int, tenor: str, *,
trade_date: pd.Timestamp=pd.Timestamp.today().normalize()):
super().__init__(index_type, series, [tenor], trade_date=trade_date)
self.tranche_quotes = get_tranche_quotes(index_type, series, tenor, trade_date.date())
index_desc = self.index_desc.reset_index('maturity').set_index('tenor')
self.maturity = index_desc.loc[tenor].maturity
self.start_date, self.cs = credit_schedule(trade_date, tenor[:-1], 1, self.yc, self.maturity)
self.K_orig = np.hstack((0., self.tranche_quotes.detach)) / 100
self.K = adjust_attachments(self.K_orig, self.cumloss, self.factor)
if index_type == "HY":
self.tranche_quotes['quotes'] = 1 - self.tranche_quotes.trancheupfrontmid / 100
else:
self.tranche_quotes['quotes'] = self.tranche_quotes.trancheupfrontmid / 100
self.tranche_quotes['running'] = self.tranche_quotes.trancherunningmid * 1e-4
if index_type == "XO":
coupon = 500 * 1e-4
self.tranche_quotes.quotes.iat[3] = self._snacpv(
self.tranche_quotes.running.iat[3], coupon, 0.4)
self.tranche_quotes.running = coupon
if index_type == "EU":
if series >= 21:
coupon = 100 * 1e-4
for i in [2, 3]:
self.tranche_quotes.quotes.iat[i] = self._snacpv(
self.tranche_quotes.running.iat[i],
coupon,
0. if i == 2 else 0.4)
self.tranche_quotes.running.iat[i] = coupon
elif series == 9:
for i in [3, 4, 5]:
coupon = 25 * 1e-4 if i == 5 else 100 * 1e-4
recov = 0.4 if i == 5 else 0
self.tranche_quotes.quotes.iat[i] = self._snacpv(
self.tranche_quotes.running.iat[i],
coupon,
recov)
self.tranche_quotes.running.iat[i] = coupon
accrued = cds_accrued(self.trade_date, self.tranche_quotes.running)
self.tranche_quotes.quotes -= accrued
self._Ngh = 250
self._Ngrid = 201
self._Z, self._w = GHquad(self._Ngh)
self.rho = np.full(self.K.size, np.nan)
def tranche_factors(self):
return np.diff(self.K) / np.diff(self.K_orig) * self.factor
def _get_quotes(self):
refprice = self.tranche_quotes.indexrefprice.iat[0]
refspread = self.tranche_quotes.indexrefspread.iat[0]
if refprice is not None:
return {self.maturity: 1 - refprice / 100}
if refspread is not None:
return {self.maturity:
self._snacpv(refspread * 1e-4, self.coupon(self.maturity), self.recovery)}
raise ValueError("ref is missing")
def _snacpv(self, spread, coupon, recov):
return upfront_charge(self.trade_date, self.value_date, self.start_date,
self.step_in_date, self.start_date, self.maturity,
coupon, self.yc, spread, recov)
@property
def default_prob(self):
sm, tickers = super().survival_matrix(self.cs.index.values.astype('M8[D]').view('int') + 134774)
return pd.DataFrame(1 - sm, index=tickers, columns=self.cs.index)
def tranche_legs(self, K, rho, complement=False, shortened=0):
if ((K == 0. and not complement) or (K == 1. and complement)):
return 0., 0.
elif ((K == 1. and not complement) or (K == 0. and complement)):
return self.index_pv()[:-1]
else:
if shortened > 0:
default_prob = self.default_prob.values[:,:-shortened]
cs = self.cs[:-shortened]
else:
default_prob = self.default_prob.values
cs = self.cs
L, R = BCloss_recov_dist(default_prob,
self.weights,
self.recovery_rates,
rho,
self._Z, self._w, self._Ngrid)
if complement:
return tranche_cl(L, R, cs, K, 1.), tranche_pl(L, cs, K, 1.)
else:
return tranche_cl(L, R, cs, 0., K), tranche_pl(L, cs, 0., K)
def tranche_pvs(self, protection=False, complement=False, shortened=0):
cl = np.zeros(self.rho.size)
pl = np.zeros(self.rho.size)
i = 0
for rho, k in zip(self.rho, self.K):
cl[i], pl[i] = self.tranche_legs(k, rho, complement, shortened)
i += 1
dK = np.diff(self.K)
pl = np.diff(pl) / dK
cl = np.diff(cl) / dK * self.tranche_quotes.running.values
if complement:
pl *= -1
cl *= -1
if protection:
bp = -pl -cl
else:
bp = 1 + pl + cl
return cl, pl, bp
def index_pv(self, discounted=True, shortened=0):
if shortened > 0:
DP = self.default_prob.values[:,-shortened]
df = self.cs.df.values[:-shortened]
coupons = self.cs.coupons.values[:-shortened]
else:
DP = self.default_prob.values
df = self.cs.df.values
coupons = self.cs.coupons
ELvec = self.weights * (1 - self.recovery_rates) @ DP
size = 1 - self.weights @ DP
sizeadj = 0.5 * (np.hstack((1., size[:-1])) + size)
if not discounted:
pl = - ELvec[-1]
cl = coupons @ sizeadj
else:
pl = - np.diff(np.hstack((0., ELvec))) @ df
cl = coupons @ (sizeadj * df)
bp = 1 + cl * self.coupon(self.maturity) + pl
return cl, pl, bp
def expected_loss(self, discounted=True, shortened=0):
if shortened > 0:
DP = self.default_prob.values[:,:-shortened]
df = self.cs.df.values[:-shortened]
else:
DP = self.default_prob.values
df = self.cs.df.values
ELvec = self.weights * (1 - self.recovery_rates) @ DP
if not discounted:
return ELvec[-1]
else:
return np.diff(np.hstack((0., ELvec))) @ df
def expected_loss_trunc(self, K, rho=None, shortened=0):
if rho is None:
rho = expit(self._skew(logit(K)))
if shortened > 0:
DP = self.default_prob.values[:,:-shortened]
df = self.cs.df.values[:-shortened]
else:
DP = self.default_prob.values
df = self.cs.df.values
ELt, _ = BCloss_recov_trunc(DP,
self.weights,
self.recovery_rates,
rho,
K,
self._Z, self._w, self._Ngrid)
return - np.dot(np.diff(np.hstack((K, ELt))), df)
def probability_trunc(self, K, rho=None, shortened=0):
if rho is None:
rho = expit(self._skew(logit(K)))
L, _ = BCloss_recov_dist(self.default_prob.values[:,-(1+shortened),np.newaxis],
self.weights,
self.recovery_rates,
rho,
self._Z, self._w, self._Ngrid)
p = np.cumsum(L)
support = np.linspace(0, 1, self._Ngrid)
probfun = PchipInterpolator(support, p)
return probfun(K)
@property
def recovery_rates(self):
return np.array([c.recovery_rates[0] for c in self.curves])
def tranche_durations(self, complement=False):
cl, _, _ = self.tranche_pvs(complement=complement)
durations = (cl - cds_accrued(self.trade_date, self.tranche_quotes.running)) / \
self.tranche_quotes.running
durations.index = self._row_names
durations.name = 'duration'
return durations
@property
def _row_names(self):
""" return pretty row names based on attach-detach"""
ad = (self.K_orig * 100).astype('int')
return [f"{a}-{d}" for a, d in zip(ad, ad[1:])]
def tranche_thetas(self, complement=False, shortened=4, method='ATM'):
_, _, bp = self.tranche_pvs(complement=complement)
rho_saved = self.rho
self.rho = self.map_skew(self, method, shortened)
_, _, bpshort = self.tranche_pvs(complement=complement, shortened=shortened)
self.rho = rho_saved
thetas = bpshort - bp + self.tranche_quotes.running.values
return pd.Series(thetas, index=self._row_names, name='theta')
def tranche_fwd_deltas(self, complement=False, shortened=4, method='ATM'):
index_short = deepcopy(self)
if shortened > 0:
index_short.cs = self.cs[:-shortened]
else:
index_short.cs = self.cs
index_short.rho = self.map_skew(index_short, method)
df = index_short.tranche_deltas()
df.columns = ['fwd_delta', 'fwd_gamma']
return df
def tranche_deltas(self, complement=False):
eps = 1e-4
self._Ngrid = 301
index_list = [self]
for tweak in [eps, -eps, 2*eps]:
tb = deepcopy(self)
tb.tweak_portfolio(tweak, self.maturity)
index_list.append(tb)
bp = np.empty((len(index_list), self.K.size - 1))
indexbp = np.empty(len(index_list))
for i, index in enumerate(index_list):
indexbp[i] = index.index_pv()[2]
bp[i] = index.tranche_pvs()[2]
factor = self.tranche_factors() / self.factor
deltas = (bp[1] - bp[2]) / (indexbp[1] - indexbp[2]) * factor
deltasplus = (bp[3] - bp[0]) / (indexbp[3] - indexbp[0]) * factor
gammas = (deltasplus - deltas) / (indexbp[1] - indexbp[0]) / 100
return pd.DataFrame({'delta': deltas, 'gamma': gammas},
index=self._row_names)
def build_skew(self, skew_type="bottomup"):
assert(skew_type == "bottomup" or skew_type == "topdown")
dK = np.diff(self.K)
def aux(rho, obj, K, quote, spread, complement):
cl, pl = obj.tranche_legs(K, rho, complement)
return pl + cl * spread + quote
if skew_type == "bottomup":
for j in range(len(dK) - 1):
cl, pl = self.tranche_legs(self.K[j], self.rho[j])
q = self.tranche_quotes.quotes.iat[j] * dK[j] - \
pl - cl * self.tranche_quotes.running.iat[j]
x0, r = brentq(aux, 0., 1.,
args=(self, self.K[j+1], q, self.tranche_quotes.running.iat[j], False),
full_output=True)
if r.converged:
self.rho[j+1] = x0
else:
print(r.flag)
break
elif skew_type == "topdown":
for j in range(len(dK) - 1, 0, -1):
cl, pl = self.tranche_legs(self.K[j+1], self.rho[j+1])
q = self.tranche_quotes.quotes.iat[j] * dK[j] - \
pl - cl * self.tranche_quotes.running.iat[j]
x0, r = brentq(aux, 0., 1.,
args=(self, self.K[j], q, self.tranche_quotes.running.iat[j], False),
full_output=True)
if r.converged:
self.rho[j+1] = x0
else:
print(res.flag)
break
self._skew = CubicSpline(logit(self.K[1:-1]),
logit(self.rho[1:-1]), bc_type='natural')
def map_skew(self, index2, method="ATM", shortened=0):
def aux(x, index1, el1, index2, el2, K2, shortened):
if x == 0. or x == 1.:
newrho = x
else:
newrho = expit(index1._skew(logit(x)))
assert newrho >= 0 and newrho <= 1, "Something went wrong"
return self.expected_loss_trunc(x, rho=newrho) /el1 - \
index2.expected_loss_trunc(K2, newrho, shortened) / el2
def aux2(x, index1, index2, K2, shortened):
newrho = expit(index1._skew(logit(x)))
assert newrho >= 0 and newrho <=1, "Something went wrong"
return np.log(self.probability_trunc(x, newrho)) - \
np.log(index2.probability_trunc(K2, newrho, shortened))
if method not in ["ATM", "TLP", "PM"]:
raise ValueError("method needs to be one of 'ATM', 'TLP' or 'PM'")
if method in ["ATM", "TLP"]:
el1 = self.expected_loss()
el2 = index2.expected_loss(shortened=shortened)
if method == "ATM":
K1eq = el1 / el2 * index2.K[1:-1]
elif method == "TLP":
K1eq = []
for K2 in index2.K[1:-1]:
K1eq.append(brentq(aux, 0., 1., (self, el1, index2, el2, K2, shortened)))
K1eq = np.array(K1eq)
elif method == "PM":
K1eq = []
for K2 in index2.K[1:-1]:
# need to figure out a better way of setting the bounds
K1eq.append(brentq(aux2, K2 * 0.1, K2 * 2.5,
(self, index2, K2, shortened)))
return np.hstack([np.nan, expit(self._skew(logit(K1eq))), np.nan])
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