from .basket_index import BasketIndex from .tranche_functions import ( credit_schedule, adjust_attachments, GHquad, BCloss_recov_dist, BCloss_recov_trunc, tranche_cl, tranche_pl) from .index_data import get_tranche_quotes from cityhash import CityHash64 from collections import namedtuple from copy import deepcopy from lru import LRU from pyisda.date import cds_accrued from scipy.optimize import brentq from scipy.interpolate import CubicSpline, PchipInterpolator from scipy.special import logit, expit import datetime import pandas as pd import numpy as np _cache = LRU(64) def BCloss_recov_dist_cached(default_prob, weights, recovery_rates, rho, Z, w, Ngrid): h = CityHash64(default_prob.T) ^ CityHash64(weights) ^ \ CityHash64(recovery_rates) ^ hash(rho) if h in _cache: return _cache[h] else: _cache[h] = BCloss_recov_dist(default_prob, weights, recovery_rates, rho, Z, w, Ngrid) return _cache[h] class DualCorrTranche(BasketIndex): def __init__(self, index_type: str, series: int, tenor: str, *, attach: float, detach: float, corr_attach: float, corr_detach: float, tranche_running: float, notional: float=10_000_000, value_date: pd.Timestamp=pd.Timestamp.today().normalize()): super().__init__(index_type, series, [tenor], value_date=value_date) self.tenor = tenor self.K_orig = np.array([attach, detach]) / 100 self.attach, self.detach = attach, detach self.K = adjust_attachments(self.K_orig, self.cumloss, self.factor) self._Ngh = 250 self._Ngrid = 201 self._Z, self._w = GHquad(self._Ngh) self.rho = np.array([corr_attach, corr_detach]) self.notional = notional self.tranche_running = tranche_running self._direction = -1. if notional > 0 else 1. self.start_date, self.cs = credit_schedule(value_date, self.tenor[:-1], 1., self.yc) self.default_prob, _ = super().survival_matrix(self.cs.index.values.astype('M8[D]'). view('int') + 134774) self._accrued = cds_accrued(value_date, self.tranche_running * 1e-4) value_date = property(BasketIndex.value_date.__get__) @value_date.setter def value_date(self, d: pd.Timestamp): BasketIndex.value_date.__set__(self, d) self.start_date, self.cs = credit_schedule(d, self.tenor[:-1], 1., self.yc) self.default_prob, _ = super().survival_matrix(self.cs.index.values.astype('M8[D]'). view('int') + 134774) self._accrued = cds_accrued(d, self.tranche_running * 1e-4) def tranche_legs(self, K, rho): if K == 0.: return 0., 0. elif K == 1.: return self.index_pv()[:-1] elif np.isnan(rho): raise ValueError("rho needs to be a real number between 0. and 1.") else: L, R = BCloss_recov_dist_cached(self.default_prob, self.weights, self.recovery_rates, rho, self._Z, self._w, self._Ngrid) Legs = namedtuple('TrancheLegs', 'coupon_leg, protection_leg') return Legs(tranche_cl(L, R, self.cs, 0., K), tranche_pl(L, self.cs, 0., K)) @property def direction(self): if self._direction == -1.: return "Buyer" else: return "Seller" @direction.setter def direction(self, d): if d == "Buyer": self._direction = -1. elif d == "Seller": self._direction = 1. else: raise ValueError("Direction needs to be either 'Buyer' or 'Seller'") @property def pv(self): """ computes coupon leg, protection leg and bond price. coupon leg is *dirty*. bond price is *clean*.""" cl = np.zeros(2) pl = np.zeros(2) i = 0 for rho, k in zip(self.rho, self.K): cl[i], pl[i] = self.tranche_legs(k, rho) i += 1 dK = np.diff(self.K) pl = np.diff(pl) / dK cl = np.diff(cl) / dK * self.tranche_running * 1e-4 bp = 1 + pl + cl - self._accrued Pvs = namedtuple('TranchePvs', 'coupon_leg, protection_leg, bond_price') return Pvs(cl, pl, bp) def reset_pv(self): self._original_pv = self.pv.bond_price self._trade_date = self._value_date def pnl(self): if self._original_pv is None: raise ValueError("original pv not set") else: # TODO: handle factor change days_accrued = (self.value_date - self._trade_date).days / 360 return self.notional * self._direction * (self.pv.bond_price - self._original_pv + self.tranche_running * days_accrued) def shock(self, params=['pnl'], *, corr_shock, kwargs): pass class TrancheBasket(BasketIndex): def __init__(self, index_type: str, series: int, tenor: str, *, value_date: pd.Timestamp=pd.Timestamp.today().normalize()): super().__init__(index_type, series, [tenor], value_date=value_date) self.tenor = tenor index_desc = self.index_desc.reset_index('maturity').set_index('tenor') self.maturity = index_desc.loc[tenor].maturity.date() self._get_tranche_quotes(value_date) self.K_orig = np.hstack((0., self.tranche_quotes.detach)) / 100 self.K = adjust_attachments(self.K_orig, self.cumloss, self.factor) self._Ngh = 250 self._Ngrid = 201 self._Z, self._w = GHquad(self._Ngh) self.rho = np.full(self.K.size, np.nan) def _get_tranche_quotes(self, value_date): self.start_date, self.cs = credit_schedule(value_date, self.tenor[:-1], 1, self.yc, self.maturity) if isinstance(value_date, datetime.datetime): value_date = value_date.date() df = get_tranche_quotes(self.index_type, self.series, self.tenor, value_date) if df.empty: raise ValueError else: self.tranche_quotes = df if self.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 self.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 self.index_type == "EU": if self.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 self.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 self._accrued = np.array([cds_accrued(self.value_date, r) for r in self.tranche_quotes.running]) self.tranche_quotes.quotes -= self._accrued value_date = property(BasketIndex.value_date.__get__) @value_date.setter def value_date(self, d: pd.Timestamp): BasketIndex.value_date.__set__(self, d) try: self._get_tranche_quotes(d) except ValueError as e: self._accrued = np.array([cds_accrued(self.value_date, r) for r in self.tranche_quotes.running]) raise ValueError(f"no tranche quotes available for date {d}") from e def tranche_factors(self): return np.diff(self.K) / np.diff(self.K_orig) * self.factor def _get_quotes(self, spread=None): if spread is not None: return {self.maturity: self._snacpv(spread * 1e-4, self.coupon(self.maturity), self.recovery)} 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") @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] elif np.isnan(rho): raise ValueError("rho needs to be a real number between 0. and 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) Legs = namedtuple('TrancheLegs', 'coupon_leg, protection_leg') if complement: return Legs(tranche_cl(L, R, cs, K, 1.), tranche_pl(L, cs, K, 1.)) else: return Legs(tranche_cl(L, R, cs, 0., K), tranche_pl(L, cs, 0., K)) def tranche_pvs(self, protection=False, complement=False, shortened=0): """ computes coupon leg, protection leg and bond price. coupon leg is *dirty*. bond price is *clean*.""" 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 + self._accrued else: bp = 1 + pl + cl - self._accrued Pvs = namedtuple('TranchePvs', 'coupon_leg, protection_leg, bond_price') return Pvs(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 Pvs = namedtuple('IndexPvs', 'coupon_leg, protection_leg, bond_price') return Pvs(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) def tranche_durations(self, complement=False): cl = self.tranche_pvs(complement=complement).coupon_leg durations = (cl - self._accrued) / self.tranche_quotes.running durations.index = self._row_names durations.name = 'duration' return durations def tranche_spreads(self, complement=False): cl, pl, _ = self.tranche_pvs(complement=complement) durations = (cl - self._accrued) / self.tranche_quotes.running.values return pd.Series(-pl / durations * 1e4, index=self._row_names, name='spread') @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).bond_price rho_saved = self.rho self.rho = self.map_skew(self, method, shortened) bpshort = self.tranche_pvs(complement=complement, shortened=shortened).bond_price 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().bond_price bp[i] = index.tranche_pvs().bond_price 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])