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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 quantlib.time.api import (
Date, Period, Days, Months, Years, UnitedStates, Actual365Fixed, Following)
from quantlib.termstructures.yields.api import YieldTermStructure
from quantlib.indexes.swap.usd_libor_swap import UsdLiborSwapIsdaFixAm
from quantlib.experimental.coupons.swap_spread_index import SwapSpreadIndex
from quantlib.experimental.coupons.lognormal_cmsspread_pricer import \
LognormalCmsSpreadPricer
from quantlib.experimental.coupons.cms_spread_coupon import \
CappedFlooredCmsSpreadCoupon
from quantlib.termstructures.volatility.api import (
VolatilityType, SwaptionVolatilityMatrix)
from quantlib.cashflows.linear_tsr_pricer import LinearTsrPricer
from quantlib.quotes import SimpleQuote
from quantlib.math.matrix import Matrix
from scipy.interpolate import RectBivariateSpline
from db import dbconn
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))
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'
with conn.cursor() as c:
c.execute(sql_str, (fixing_date,))
try:
fixing1, fixing2 = next(c)
except StopIteration:
raise RuntimeError(f"no fixings available for date {fixing_date}")
else:
sql_str = f'SELECT fixing_date, "{tenor1}y" ,"{tenor2}y" FROM USD_swap_fixings ' \
'ORDER BY fixing_date DESC LIMIT 1'
with conn.cursor() as c:
c.execute(sql_str, fixing_date)
fixing_date, fixing1, fixing2 = next(c)
date = Date.from_datetime(fixing_date)
fixing1 = float(fixing1)
fixing2 = float(fixing2)
return date, fixing1, fixing2
def build_spread_index(tenor1, tenor2):
yc = YieldTermStructure()
USISDA1 = UsdLiborSwapIsdaFixAm(Period(tenor1, Years), yc)
USISDA2 = UsdLiborSwapIsdaFixAm(Period(tenor2, Years), yc)
spread_index = SwapSpreadIndex(f"{tenor1}-{tenor2}", USISDA1, USISDA2)
return spread_index, yc
def get_swaption_vol_data(source="ICPL", vol_type=VolatilityType.ShiftedLognormal,
date=None):
if vol_type == VolatilityType.Normal:
table_name = "swaption_normal_vol"
else:
table_name = "swaption_lognormal_vol"
sql_str = f"SELECT * FROM {table_name} WHERE source=%s "
if date is None:
sql_str += "ORDER BY date DESC LIMIT 1"
params = (source,)
else:
sql_str += "AND date=%s"
params = (source, date)
conn = dbconn('serenitasdb')
with conn.cursor() as c:
c.execute(sql_str, params)
surf_data = next(c)
return surf_data[0], np.array(surf_data[1:-1], order='F').T
def get_swaption_vol_surface(date, vol_type):
date, surf, _ = get_swaption_vol_data(date=date, vol_type=vol_type)
tenors = [1/12, 0.25, 0.5, 0.75] + list(range(1, 11)) + [15., 20., 25., 30.]
return RectBivariateSpline(tenors, tenors[-14:], surf)
def get_swaption_vol_matrix(date, data, vol_type=VolatilityType.ShiftedLognormal):
# figure out what to do with nan
calendar = UnitedStates()
data = np.delete(data, 3, axis=0) / 100
m = Matrix.from_ndarray(data)
option_tenors = [Period(i, Months) for i in [1, 3, 6]] + \
[Period(i, Years) for i in range(1, 11)] + \
[Period(i, Years) for i in [15, 20, 25, 30]]
swap_tenors = option_tenors[-14:]
return (SwaptionVolatilityMatrix.
from_reference_date(Date.from_datetime(date),
calendar,
Following,
option_tenors,
swap_tenors,
m,
Actual365Fixed(),
vol_type=vol_type))
def quantlib_model(date, spread_index, yc, cap, rho, maturity, mean_rev=0.,
vol_type=VolatilityType.ShiftedLognormal):
date, surf = get_swaption_vol_data(date=date, vol_type=vol_type)
atm_vol = get_swaption_vol_matrix(date, surf, vol_type)
pricer = LinearTsrPricer(atm_vol, SimpleQuote(mean_rev), yc)
vol_type = VolatilityType(atm_vol.volatility_type)
cmsspread_pricer = LognormalCmsSpreadPricer(pricer,
SimpleQuote(rho),
yc)
end_date = Date.from_datetime(maturity)
pay_date = spread_index.fixing_calendar.advance(end_date, 0, Days)
start_date = end_date - Period(1, Years)
end_date = Date(19, 1, 2020)
cms_spread_coupon = CappedFlooredCmsSpreadCoupon(
pay_date, 300_000_000, start_date, end_date,
spread_index.fixing_days, spread_index, 1., -cap,
floor=0.,
day_counter=Actual365Fixed(),
is_in_arrears=True)
cms_spread_coupon.set_pricer(cmsspread_pricer)
return cms_spread_coupon
def plot_surf(surf, tenors):
xx, yy = np.meshgrid(tenors, tenors[-14:])
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(xx, yy, surf.ev(xx, yy))
def globeop_model(date, spread_index, yc, strike, rho, maturity,
vol_type=VolatilityType.Normal):
""" price cap spread option without convexity adjustment
vol_type Normal is the only supported one at the moment"""
maturity = Date.from_datetime(maturity)
fixing_date = spread_index.fixing_calendar.advance(maturity, units=Days)
forward = spread_index.fixing(fixing_date)
date, surf = get_swaption_vol_data(date=date, vol_type=vol_type)
atm_vol = get_swaption_vol_matrix(date, surf, vol_type=vol_type)
d = Date.from_datetime(date)
T = Actual365Fixed().year_fraction(d, maturity)
vol1 = atm_vol.volatility(maturity, spread_index.swap_index1.tenor, 0.)
vol2 = atm_vol.volatility(maturity, spread_index.swap_index2.tenor, 0.)
vol_spread = sqrt(vol1**2 + vol2**2 - 2 * rho * vol1 * vol2)
# normal vol is not scale independent and is computed in percent terms, so we scale
# everything by 100.
return 0.01 * yc.discount(T) * bachelier(forward * 100, strike * 100, T, vol_spread)
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