diff options
| -rw-r--r-- | python/analytics/cms_spread.py | 40 | ||||
| -rw-r--r-- | python/exploration/portfolio_example.py | 8 |
2 files changed, 22 insertions, 26 deletions
diff --git a/python/analytics/cms_spread.py b/python/analytics/cms_spread.py index 7d34b7b1..32c16ed1 100644 --- a/python/analytics/cms_spread.py +++ b/python/analytics/cms_spread.py @@ -2,7 +2,8 @@ import numpy as np import matplotlib.pyplot as plt from .tranche_functions import GHquad from math import exp, sqrt, log -from .black import bachelier +from .black import bachelier, cnd_erf +from numba import jit, float64, boolean from quantlib.time.api import ( Date, Period, Days, Months, Years, UnitedStates, Actual365Fixed, Following) from quantlib.termstructures.yields.api import YieldTermStructure @@ -21,33 +22,28 @@ from quantlib.math.matrix import Matrix from scipy.interpolate import RectBivariateSpline from db import dbconn +@jit(float64(float64, float64, float64, float64, float64, float64, float64, + float64, float64, boolean), cache=True, nopython=True) +def h(z, K, S1, S2, mu_x, mu_y, sigma_x, sigma_y, rho, call=True): + # z = (y - mu_y) / sigma_y + u1 = mu_x + rho * sigma_x * z + Ktilde = K + S2 * exp(mu_y + sigma_y * z) + u2 = log(Ktilde / S1) -def CMS_spread(T_alpha, X, beta, gamma): - Z, w = GHquad(100) - return np.inner(f(Z), w) - - -def h(v, X, S_alpha_beta, mu_beta, sigma_alpha_beta, T_alpha): - r = (mu_beta - 0.5 * sigma_alpha_beta * sigma_alpha_beta) * T_alpha + \ - sigma_alpha_beta * sqrt(T_alpha) * v - return X + S_alpha_beta * exp(r) - - -def f(v, X, S_alpha_beta, S_alpha_gamma, mu_beta, mu_gamma, T_alpha, rho): - h = h(v, X, S_alpha_beta, mu_beta, sigma_alpha_beta, T_alpha) - u = rho * sigma_alpha_gamma * sqrt(T_alpha) * v - d = sigma_alpha_gamma * sqrt(T_alpha) * sqrt(1 - rho ** 2) - r = mu_gamma * T_alpha - 0.5 * rho * rho * sigma_alpha_gamma ** 2 * T_alpha + u - u0 = log(S_alpha_gamma / h) + u - u1 = u0 + (mu_gamma + (0.5 - rho ** 2) * sigma_alpha_gamma**2) * T_alpha - u2 = u0 + (mu_gamma - 0.5 * sigma_alpha_gamma**2) * T_alpha - return 0.5 * (S_alpha_gamma * exp(r) * cnd_erf(u1 / d) - h * cnd_erf(u2 / d)) + v = sigma_x * sqrt(1 - rho * rho) + v2 = sigma_x * sigma_x * (1 - rho * rho) + if call: + x = (u1 - u2) / v + return 0.5 * (S1 * exp(u1 + 0.5 * v2) * cnd_erf(x + v) - Ktilde * cnd_erf(x)) + else: + x = (u2 - u1) / v + return 0.5 * (Ktilde * cnd_erf(x) - S1 * exp(u1 + 0.5 * v2) * cnd_erf(x - v)) def get_fixings(conn, tenor1, tenor2, fixing_date=None): if fixing_date: sql_str = f'SELECT "{tenor1}y" ,"{tenor2}y" FROM USD_swap_fixings ' \ - 'WHERE fixing_date=%s' + 'WHERE fixing_date=%s' with conn.cursor() as c: c.execute(sql_str, (fixing_date,)) try: diff --git a/python/exploration/portfolio_example.py b/python/exploration/portfolio_example.py index 6b72a2c1..57bd686f 100644 --- a/python/exploration/portfolio_example.py +++ b/python/exploration/portfolio_example.py @@ -1,19 +1,19 @@ -from analytics import (Portfolio, BlackSwaption, Index, +from analytics import (Portfolio, BlackSwaption, CreditIndex, BlackSwaptionVolSurface, Swaption) from analytics.scenarios import run_portfolio_scenarios import pandas as pd import numpy as np -option_delta = Index.from_tradeid(870) +option_delta = CreditIndex.from_tradeid(870) option1 = BlackSwaption.from_tradeid(5, option_delta) option2 = BlackSwaption.from_tradeid(6, option_delta) portf = Portfolio([option1, option2, option_delta]) -date_range = pd.bdate_range(option_delta.trade_date, +date_range = pd.bdate_range(option_delta.value_date, pd.Timestamp('2017-04-19'), freq='W') vol_shock = np.arange(-0.15, 0.3, 0.01) spread_shock = np.arange(-0.2, 0.3, 0.01) -vs = BlackSwaptionVolSurface("IG", 27, trade_date=option_delta.trade_date) +vs = BlackSwaptionVolSurface("IG", 27, value_date=option_delta.value_date) vol_surface = vs[vs.list()[-1]] df = run_portfolio_scenarios(portf, date_range, spread_shock, vol_shock, vol_surface, ['pv', 'delta']) |