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-rw-r--r--python/analytics/cms_spread.py44
-rw-r--r--python/exploration/test_cms.py129
2 files changed, 135 insertions, 38 deletions
diff --git a/python/analytics/cms_spread.py b/python/analytics/cms_spread.py
index e518c498..402d0413 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 math import exp, sqrt, log
from .black import bachelier, cnd_erf
-from numba import cfunc, int64, float64, boolean, types
+from numba import (cfunc, types, jit, float64, boolean,
+ optional, vectorize)
from quantlib.time.api import (
Date, Period, Days, Months, Years, UnitedStates, Actual365Fixed, Following)
from quantlib.termstructures.yields.api import YieldTermStructure
@@ -20,26 +21,35 @@ from quantlib.quotes import SimpleQuote
from quantlib.math.matrix import Matrix
from scipy.interpolate import RectBivariateSpline
from db import dbconn
-from numba import cfunc
-# @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)
+@vectorize([float64(float64, float64, float64, float64, float64, float64, float64,
+ float64, float64)], cache=True, nopython=True)
+def h_call(z, K, S1, S2, mu_x, mu_y, sigma_x, sigma_y, rho):
+ # 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)
-# 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))
+ v = sigma_x * sqrt(1 - rho * rho)
+ v2 = sigma_x * sigma_x * (1 - rho * rho)
+ x = (u1 - u2) / v
+ return 0.5 * (S1 * exp(u1 + 0.5 * v2) * cnd_erf(x + v) - Ktilde * cnd_erf(x))
+
+@vectorize([float64(float64, float64, float64, float64, float64, float64, float64,
+ float64, float64)], cache=True, nopython=True)
+def h_put(z, K, S1, S2, mu_x, mu_y, sigma_x, sigma_y, rho,):
+ # 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)
+
+ v = sigma_x * sqrt(1 - rho * rho)
+ v2 = sigma_x * sigma_x * (1 - rho * rho)
+ x = (u2 - u1) / v
+ return 0.5 * (Ktilde * cnd_erf(x) - S1 * exp(u1 + 0.5 * v2) * cnd_erf(x - v))
sig = types.double(types.intc, types.CPointer(types.double))
+
@cfunc(sig, cache=True, nopython=True)
def h1(n, args):
z = args[0]
diff --git a/python/exploration/test_cms.py b/python/exploration/test_cms.py
index 4705e01e..205ca670 100644
--- a/python/exploration/test_cms.py
+++ b/python/exploration/test_cms.py
@@ -1,26 +1,113 @@
from analytics.cms_spread import (
- quantlib_model, globeop_model, build_spread_index, VolatilityType)
+ quantlib_model, globeop_model, build_spread_index, VolatilityType,
+ get_swaption_vol_data, get_swaption_vol_matrix)
from yieldcurve import YC
import pandas as pd
-from quantlib.time.api import Date
-swap_index_30y2y, yc = build_spread_index(30, 2)
+from quantlib.time.api import Date, Period, Years, Days, ModifiedFollowing
+from quantlib.cashflows.cms_coupon import CmsCoupon
+from quantlib.experimental.coupons.cms_spread_coupon import (
+ CmsSpreadCoupon, CappedFlooredCmsSpreadCoupon)
+import datetime
+import math
+# swap_index_30y2y, yc = build_spread_index(30, 2)
+# cap = 0.00758
+# corr = 0.8
+# r = []
+# maturity = pd.Timestamp("2020-01-19")
+# today = pd.Timestamp.today()
+
+# for d in pd.bdate_range("2018-01-19", today, closed="left", normalize=True):
+# d = pd.Timestamp("2018-01-19")
+# yc.link_to(YC(evaluation_date=d.date()))
+# yc.extrapolation = True
+# if d == pd.Timestamp("2018-02-16"):
+# continue
+# capped_floored_cms_spread_coupon_ln = \
+# quantlib_model(d, swap_index_30y2y, yc, cap, corr, maturity)
+# rate1 = capped_floored_cms_spread_coupon_ln.rate
+# cms_spread_coupon_n = quantlib_model(d, swap_index_30y2y, yc, cap, corr, maturity,
+# VolatilityType.Normal)
+# rate2 = cms_spread_coupon_n.rate
+# rate3 = globeop_model(d, swap_index_30y2y, yc, cap, corr - 0.075, maturity)
+# # df = pd.DataFrame(r, columns=['date', 'QL_ln', 'QL_n', 'Globeop']).set_index('date')
+
+# try to get convexity adjustement
+from quantlib.indexes.swap.usd_libor_swap import UsdLiborSwapIsdaFixAm
+from quantlib.cashflows.conundrum_pricer import AnalyticHaganPricer, YieldCurveModel
+from quantlib.quotes import SimpleQuote
+from quantlib.time.api import Actual365Fixed
+# trade_date = datetime.date(2018, 1, 19)
+trade_date = datetime.date(2018, 8, 23)
+maturity = Date.from_datetime(trade_date) + Period(2, Years)
+spread_index, yc = build_spread_index(30, 2)
+yc.link_to(YC(evaluation_date=trade_date))
+yc.extrapolation = True
+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)
+
cap = 0.00758
-corr = 0.8
-r = []
-maturity = pd.Timestamp("2020-01-19")
-today = pd.Timestamp.today()
+cms2y30y_cap = CappedFlooredCmsSpreadCoupon(
+ payment_date,
+ 100_000_000,
+ start_date=accrued_start_date,
+ end_date=accrued_end_date,
+ fixing_days=spread_index.fixing_days,
+ index=spread_index,
+ gearing=1.,
+ spread=-cap,
+ floor=0.,
+ day_counter=Actual365Fixed(),
+ is_in_arrears=True)
+
+date, surf = get_swaption_vol_data(date=trade_date, vol_type=VolatilityType.ShiftedLognormal)
+atm_vol = get_swaption_vol_matrix(trade_date, surf)
+μ = SimpleQuote(0.1)
+from quantlib.experimental.coupons.lognormal_cmsspread_pricer import LognormalCmsSpreadPricer
+corr = SimpleQuote(0.8)
+cms_pricer = AnalyticHaganPricer(atm_vol, YieldCurveModel.Standard, μ)
+spread_pricer = LognormalCmsSpreadPricer(
+ cms_pricer,
+ corr,
+ integration_points=20)
+cms2y30y_cap.set_pricer(spread_pricer)
+fixing_time = atm_vol.time_from_reference(cms2y30y_cap.fixing_date)
+cms30y = CmsCoupon(payment_date,
+ 100_000_000,
+ start_date=accrued_start_date,
+ end_date=accrued_end_date,
+ fixing_days=2,
+ index=spread_index.swap_index1,
+ is_in_arrears=True)
+cms2y = CmsCoupon(payment_date,
+ 100_000_000,
+ start_date=accrued_start_date,
+ end_date=accrued_end_date,
+ fixing_days=2,
+ index=spread_index.swap_index2,
+ is_in_arrears=True)
+cms30y.set_pricer(cms_pricer)
+cms2y.set_pricer(cms_pricer)
+s1 = cms30y.index_fixing
+s2 = cms2y.index_fixing
+adjusted1 = cms30y.rate
+adjusted2 = cms2y.rate
+import math
+T_alpha = atm_vol.time_from_reference(cms2y30y_cap.fixing_date)
+mu1 = 1 / T_alpha * math.log(adjusted1 / s1)
+mu2 = 1 / T_alpha * math.log(adjusted2 / s2)
+vol1 = atm_vol.volatility(cms2y.fixing_date, spread_index.swap_index1.tenor, s1)
+vol2 = atm_vol.volatility(cms30y.fixing_date, spread_index.swap_index2.tenor, s2)
+mu_x = (mu1 - 0.5 * vol1 ** 2) * T_alpha
+mu_y = (mu2 - 0.5 * vol2 ** 2) * T_alpha
+sigma_x = vol1 * math.sqrt(T_alpha)
+sigma_y = vol2 * math.sqrt(T_alpha)
-for d in pd.bdate_range("2018-01-19", today, closed="left", normalize=True):
- d = pd.Timestamp("2018-01-19")
- yc.link_to(YC(evaluation_date=d.date()))
- yc.extrapolation = True
- if d == pd.Timestamp("2018-02-16"):
- continue
- capped_floored_cms_spread_coupon_ln = \
- quantlib_model(d, swap_index_30y2y, yc, cap, corr, maturity)
- rate1 = capped_floored_cms_spread_coupon_ln.rate
- cms_spread_coupon_n = quantlib_model(d, swap_index_30y2y, yc, cap, corr, maturity,
- VolatilityType.Normal)
- rate2 = cms_spread_coupon_n.rate
- rate3 = globeop_model(d, swap_index_30y2y, yc, cap, corr - 0.075, maturity)
-# df = pd.DataFrame(r, columns=['date', 'QL_ln', 'QL_n', 'Globeop']).set_index('date')
+from scipy.special import roots_hermitenorm
+from analytics.cms_spread import h_call, h_put
+import numpy as np
+x, w = roots_hermitenorm(16)
+val_put = 1/math.sqrt(2*math.pi) * np.dot(w, h_put(x, cap, s1, s2, mu_x, mu_y, sigma_x, sigma_y, corr.value))
+val_call = 1/math.sqrt(2*math.pi) * np.dot(w, h_call(x, cap, s1, s2, mu_x, mu_y, sigma_x, sigma_y, corr.value))
+print(cms2y30y_cap.rate, cms2y30y_cap.underlying.rate + val_put, val_call)
generated by cgit v1.2.3-70-g09d2 (git 2.52.0) at 2025-12-24 10:56:07 +0000