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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,
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
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.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):
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:
L, R = BCloss_recov_dist(self.default_prob.values,
self.weights,
self.recovery_rates,
rho,
self._Z, self._w, self._Ngrid)
if complement:
return tranche_cl(L, R, self.cs, K, 1.), tranche_pl(L, self.cs, K, 1.)
else:
return tranche_cl(L, R, self.cs, 0., K), tranche_pl(L, self.cs, 0., K)
def tranche_pvs(self, protection=False, complement=False):
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)
i += 1
dK = np.diff(self.K)
pl = np.diff(pl) / dK
cl = np.diff(cl) / dK * self.tranche_quotes.running
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):
DP = self.default_prob.values
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 = self.cs.coupons.values() @ sizeadj
else:
pl = - np.diff(np.hstack((0., ELvec))) @ self.cs.df.values
cl = self.cs.coupons.values @ (sizeadj * self.cs.df.values)
bp = 1 + cl * self.coupon(self.maturity) + pl
return cl, pl, bp
@property
def recovery_rates(self):
return np.array([c.recovery_rates[0] for c in self.curves])
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.zeros((len(index_list), self.K.size - 1))
indexbp = np.zeros(len(index_list))
for i, index in enumerate(index_list):
indexbp[i] = index.index_pv()[2]
bp[i] = index.tranche_pvs(complement)[2]
deltas = (bp[1] - bp[2]) / (indexbp[1] - indexbp[2]) * self.tranche_factors() / self.factor
deltasplus = (bp[3] - bp[0]) / (indexbp[3]-indexbp[0]) * self.tranche_factors() / self.factor
gammas = (deltasplus - deltas) / (indexbp[1] - indexbp[0]) / 100
return pd.DataFrame({'delta': deltas, 'gamma': gammas},
index=self.tranche_quotes[['attach', 'detach']].
apply(lambda row: f'{row.attach}-{row.detach}',
axis=1))
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
|
