diff options
Diffstat (limited to 'python/analytics')
| -rw-r--r-- | python/analytics/tranche_basket.py | 65 |
1 files changed, 59 insertions, 6 deletions
diff --git a/python/analytics/tranche_basket.py b/python/analytics/tranche_basket.py index 53514824..83b69508 100644 --- a/python/analytics/tranche_basket.py +++ b/python/analytics/tranche_basket.py @@ -2,12 +2,14 @@ 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) + 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 +from scipy.special import logit, expit import pandas as pd import numpy as np @@ -117,20 +119,58 @@ class TrancheBasket(BasketIndex): bp = 1 + pl + cl return cl, pl, bp - def index_pv(self, discounted=True): - DP = self.default_prob.values + 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 = self.cs.coupons.values() @ sizeadj + cl = coupons @ sizeadj else: - pl = - np.diff(np.hstack((0., ELvec))) @ self.cs.df.values - cl = self.cs.coupons.values @ (sizeadj * self.cs.df.values) + 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): + if rho is None: + rho = expit(self._skew(logit(K))) + L, _ = BCloss_recov_dist(self.default_prob.values, + self.weights, + self.recovery_rates, + rho, + self._Z, self._w, self._Ngrid) + Ltrunc, _ = BCloss_recov_trunc(self.default_prob.values, + self.weights, + self.recovery_rates, + rho, + K, + self._Z, self._w, self._Ngrid) + return - tranche_pl(L, self.cs, 0., K), Ltrunc + + @property def recovery_rates(self): return np.array([c.recovery_rates[0] for c in self.curves]) @@ -191,3 +231,16 @@ class TrancheBasket(BasketIndex): 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"): + 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() + + if method == "ATM": + K1eq = el1 / el2 * index2.K[1:-1] |