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import datetime
import math
import numpy as np
import unittest
from analytics.cms_spread import (
build_spread_index, VolatilityType,
get_swaption_vol_data, get_swaption_vol_matrix, get_cms_coupons,
get_params, _call_integrand, h_call, h_put, CmsSpread)
from quantlib.quotes import SimpleQuote
from quantlib.time.api import (Actual365Fixed, Days, Date, ModifiedFollowing,
Period, Years)
from yieldcurve import YC
from quantlib.cashflows.conundrum_pricer import (
AnalyticHaganPricer, YieldCurveModel)
from quantlib.experimental.coupons.cms_spread_coupon import (
CappedFlooredCmsSpreadCoupon)
from quantlib.experimental.coupons.lognormal_cmsspread_pricer import (
LognormalCmsSpreadPricer)
from scipy import LowLevelCallable
from scipy.special import roots_hermitenorm
from scipy.integrate import quad
import ctypes
class TestCmsSpread(unittest.TestCase):
def setUp(self):
self.trade_date = datetime.date(2018, 1, 19)
option_tenor = Period(2, Years)
maturity = Date.from_datetime(self.trade_date) + Period(2, Years)
spread_index, self.yc = build_spread_index(30, 2)
fixing_date = (spread_index.
fixing_calendar.
adjust(maturity, ModifiedFollowing))
payment_date = (spread_index.
fixing_calendar.
advance(fixing_date, 2, Days))
accrued_end_date = payment_date
accrued_start_date = accrued_end_date - Period(1, Years)
self.cap = 0.0075835
self.notional = 100_000_000
self.cms30y2y_cap = CappedFlooredCmsSpreadCoupon(
payment_date,
self.notional,
start_date=accrued_start_date,
end_date=accrued_end_date,
fixing_days=spread_index.fixing_days,
index=spread_index,
gearing=1.,
spread=-self.cap,
floor=0.,
day_counter=Actual365Fixed(),
is_in_arrears=True)
self.cms2y, self.cms30y = get_cms_coupons(self.trade_date,
self.notional,
option_tenor,
spread_index)
evaluation_date = datetime.date(2018, 8, 23)
self.yc.link_to(YC(evaluation_date=evaluation_date, extrapolation=True))
self.yc.extrapolation = True
date, surf = get_swaption_vol_data(date=evaluation_date,
vol_type=VolatilityType.ShiftedLognormal)
atm_vol = get_swaption_vol_matrix(evaluation_date, surf)
μ = SimpleQuote(0.1)
self.ρ = SimpleQuote(0.8)
self.cms_pricer = AnalyticHaganPricer(atm_vol, YieldCurveModel.Standard, μ)
self.cms2y.set_pricer(self.cms_pricer)
self.cms30y.set_pricer(self.cms_pricer)
self.params = get_params(self.cms2y, self.cms30y, atm_vol)
cms_spread_pricer = LognormalCmsSpreadPricer(
self.cms_pricer,
self.ρ,
integration_points=20)
self.cms30y2y_cap.set_pricer(cms_spread_pricer)
def test_black_model(self):
x, w = roots_hermitenorm(16)
val_call = 1 / math.sqrt(2 * math.pi) * np.dot(w,
h_call(x, self.cap, *self.params, self.ρ.value))
val_put = 1 / math.sqrt(2 * math.pi) * np.dot(w,
h_put(x, self.cap, *self.params, self.ρ.value))
self.assertAlmostEqual(self.cms30y2y_cap.rate,
val_call)
self.assertAlmostEqual(-self.cms30y2y_cap.underlying.rate, val_put - val_call)
self.assertAlmostEqual(self.cms30y.rate - self.cms2y.rate - self.cap,
self.cms30y2y_cap.underlying.rate)
def test_h1_hcall(self):
args = (self.cap, *self.params, self.ρ.value)
h1_fun = _call_integrand.function
for x in np.linspace(-5, 5, 11):
full_args = np.array((x, *args))
a = h1_fun(9, full_args.ctypes.data_as(ctypes.POINTER(ctypes.c_double)))
b = h_call(x, *args) * math.exp(-0.5 * x * x)
self.assertAlmostEqual(a, b)
def test_scipy_integrate(self):
x, w = roots_hermitenorm(20)
val_call = np.dot(w, h_call(x, self.cap, *self.params, self.ρ.value))
args = (self.cap, *self.params, self.ρ.value)
val, _ = quad(_call_integrand, -np.inf, np.inf, args=(self.cap, *self.params, self.ρ.value))
self.assertAlmostEqual(val, val_call)
def test_CmsSpread(self):
trade = CmsSpread(None, 2, 30, 0.0075835, Period(2, Years), value_date=self.trade_date)
trade1 = CmsSpread.from_tradeid(1)
trade.value_date = datetime.date(2018, 8, 23)
trade1.value_date = datetime.date(2018, 8, 23)
self.assertAlmostEqual(self.cms30y2y_cap.rate * 1e8 * self.yc.discount(self.cms2y.fixing_date),
trade.pv)
self.assertAlmostEqual(trade.pv, trade1.pv)
if __name__ == "__main__":
unittest.main()
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