def test_analytic_versus_black(self):
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 30)
exercise = EuropeanExercise(exercise_date)
risk_free_ts = flat_rate(0.1, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
s0 = SimpleQuote(32.0)
v0 = 0.05
kappa = 5.0
theta = 0.05
sigma = 1.0e-4
rho = 0.0
process = HestonProcess(
risk_free_ts, dividend_ts, s0, v0, kappa, theta, sigma, rho
)
option = VanillaOption(payoff, exercise)
engine = AnalyticHestonEngine(HestonModel(process), 144)
option.set_pricing_engine(engine)
calculated = option.net_present_value
year_fraction = daycounter.year_fraction(
settlement_date, exercise_date
)
forward_price = 32 * np.exp((0.1 - 0.04) * year_fraction)
expected = blackFormula(
payoff.type, payoff.strike, forward_price,
np.sqrt(0.05 * year_fraction)
) * np.exp(-0.1 * year_fraction)
tolerance = 2.0e-7
self.assertAlmostEqual(
calculated,
expected,
delta=tolerance
)
def setUp(self):
settlement_date = today()
settings = Settings()
settings.evaluation_date = settlement_date
daycounter = ActualActual()
self.calendar = NullCalendar()
i_rate = .1
i_div = .04
self.risk_free_ts = flat_rate(i_rate, daycounter)
self.dividend_ts = flat_rate(i_div, daycounter)
self.s0 = SimpleQuote(32.0)
# Bates model
self.v0 = 0.05
self.kappa = 5.0
self.theta = 0.05
self.sigma = 1.0e-4
self.rho = 0.0
self.Lambda = .1
self.nu = .01
self.delta = .001
def _blsimpv(price,
spot,
strike,
risk_free_rate,
time,
option_type='Call',
dividend=0.0):
spot = SimpleQuote(spot)
daycounter = ActualActual()
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), .3, daycounter)
process = BlackScholesMertonProcess(spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
accuracy = 0.001
max_evaluations = 1000
min_vol = 0.01
max_vol = 2
vol = option.implied_volatility(price, process, accuracy, max_evaluations,
min_vol, max_vol)
return vol
def test_extrapolation(self):
rate_helpers = build_helpers()
settings = Settings()
calendar = TARGET()
# must be a business Days
dtObs = date(2007, 4, 27)
eval_date = calendar.adjust(pydate_to_qldate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
print('dt Obs: %s\ndt Eval: %s\ndt Settle: %s' %
(dtObs, eval_date, settlement_date))
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-2
ts = PiecewiseYieldCurve.from_reference_date(BootstrapTrait.Discount,
Interpolator.LogLinear,
settlement_date,
rate_helpers,
ts_day_counter, tolerance)
# max_date raises an exception without extrapolaiton...
self.assertFalse(ts.extrapolation)
with self.assertRaisesRegexp(
RuntimeError, "1st iteration: failed at 2nd alive instrument"):
dtMax = ts.max_date
def test_zero_curve(self):
rate_helpers = build_helpers()
settings = Settings()
calendar = TARGET()
# must be a business Days
dtObs = date(2007, 4, 27)
eval_date = calendar.adjust(pydate_to_qldate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-2
ts = PiecewiseYieldCurve.from_reference_date(BootstrapTrait.Discount,
Interpolator.LogLinear,
settlement_date,
rate_helpers,
ts_day_counter, tolerance)
# max_date raises an exception...
ts.extrapolation = True
zr = ts.zero_rate(Date(10, 5, 2027), ts_day_counter, 2)
self.assertAlmostEqual(zr.rate, 0.0539332)
def test_smith(self):
# test against result published in
# Journal of Computational Finance Vol. 11/1 Fall 2007
# An almost exact simulation method for the heston model
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
timeToMaturity = 4
exercise_date = settlement_date + timeToMaturity * 365
c_payoff = PlainVanillaPayoff(Call, 100)
exercise = EuropeanExercise(exercise_date)
risk_free_ts = flat_rate(0., daycounter)
dividend_ts = flat_rate(0., daycounter)
s0 = SimpleQuote(100.0)
v0 = 0.0194
kappa = 1.0407
theta = 0.0586
sigma = 0.5196
rho = -.6747
nb_steps_a = 100
nb_paths = 20000
seed = 12347
process = HestonProcess(risk_free_ts, dividend_ts, s0, v0, kappa,
theta, sigma, rho, QUADRATICEXPONENTIAL)
model = HestonModel(process)
option = VanillaOption(c_payoff, exercise)
engine = AnalyticHestonEngine(model, 144)
option.set_pricing_engine(engine)
price_fft = option.net_present_value
engine = MCEuropeanHestonEngine(process,
antithetic_variate=True,
steps_per_year=nb_steps_a,
required_samples=nb_paths,
seed=seed)
option.set_pricing_engine(engine)
price_mc = option.net_present_value
expected = 15.1796
tolerance = .05
self.assertAlmostEqual(price_fft, expected, delta=tolerance)
self.assertAlmostEqual(price_mc, expected, delta=tolerance)
def test_analytic_versus_black(self):
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 30)
exercise = EuropeanExercise(exercise_date)
risk_free_ts = flat_rate(0.1, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
s0 = SimpleQuote(32.0)
v0 = 0.05
kappa = 5.0
theta = 0.05
sigma = 1.0e-4
rho = 0.0
process = HestonProcess(risk_free_ts, dividend_ts, s0, v0, kappa,
theta, sigma, rho)
option = VanillaOption(payoff, exercise)
engine = AnalyticHestonEngine(HestonModel(process), 144)
option.set_pricing_engine(engine)
calculated = option.net_present_value
year_fraction = daycounter.year_fraction(settlement_date,
exercise_date)
forward_price = 32 * np.exp((0.1 - 0.04) * year_fraction)
expected = blackFormula(payoff.type, payoff.strike, forward_price,
np.sqrt(0.05 * year_fraction)) * np.exp(
-0.1 * year_fraction)
tolerance = 2.0e-7
self.assertAlmostEqual(calculated, expected, delta=tolerance)
def test_creation(self):
settings = Settings()
# Market information
calendar = TARGET()
# must be a business day
settings.evaluation_date = calendar.adjust(today())
settlement_date = Date(18, September, 2008)
# must be a business day
settlement_date = calendar.adjust(settlement_date);
quotes = [SimpleQuote(0.0096), SimpleQuote(0.0145), SimpleQuote(0.0194)]
tenors = [3, 6, 12]
rate_helpers = []
calendar = TARGET()
deposit_day_counter = Actual365Fixed()
convention = ModifiedFollowing
end_of_month = True
for quote, month in zip(quotes, tenors):
tenor = Period(month, Months)
fixing_days = 3
helper = DepositRateHelper(
quote, tenor, fixing_days, calendar, convention, end_of_month,
deposit_day_counter
)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve[BootstrapTrait.Discount, LogLinear].from_reference_date(
settlement_date, rate_helpers,
ts_day_counter, accuracy=tolerance
)
self.assertIsNotNone(ts)
self.assertEqual( Date(18, September, 2008), ts.reference_date)
# this is not a real test ...
self.assertAlmostEqual(0.9975, ts.discount(Date(21, 12, 2008)), 4)
self.assertAlmostEqual(0.9944, ts.discount(Date(21, 4, 2009)), 4)
self.assertAlmostEqual(0.9904, ts.discount(Date(21, 9, 2009)), 4)
dates, dfs = zip(*ts.nodes)
self.assertAlmostEqual(list(dates), ts.dates)
self.assertAlmostEqual(list(dfs), ts.data)
def test_creation(self):
settings = Settings()
# Market information
calendar = TARGET()
# must be a business day
settings.evaluation_date = calendar.adjust(today())
settlement_date = Date(18, September, 2008)
# must be a business day
settlement_date = calendar.adjust(settlement_date);
quotes = [0.0096, 0.0145, 0.0194]
tenors = [3, 6, 12]
rate_helpers = []
calendar = TARGET()
deposit_day_counter = Actual365Fixed()
convention = ModifiedFollowing
end_of_month = True
for quote, month in zip(quotes, tenors):
tenor = Period(month, Months)
fixing_days = 3
helper = DepositRateHelper(
quote, tenor, fixing_days, calendar, convention, end_of_month,
deposit_day_counter
)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = term_structure_factory(
'discount', 'loglinear', settlement_date, rate_helpers,
ts_day_counter, tolerance
)
self.assertIsNotNone(ts)
self.assertEquals( Date(18, September, 2008), ts.reference_date)
# this is not a real test ...
self.assertAlmostEquals(0.9975, ts.discount(Date(21, 12, 2008)), 4)
self.assertAlmostEquals(0.9944, ts.discount(Date(21, 4, 2009)), 4)
self.assertAlmostEquals(0.9904, ts.discount(Date(21, 9, 2009)), 4)
def test_bucketanalysis_bond(self):
face_amount = 100.0
redemption = 100.0
issue_date = Date(27, January, 2011)
maturity_date = Date(1, January, 2021)
coupon_rate = 0.055
fixed_bond_schedule = Schedule.from_rule(
issue_date,
maturity_date,
Period(Semiannual),
UnitedStates(market=GovernmentBond),
Unadjusted,
Unadjusted,
Backward,
False)
bond = FixedRateBond(
self.settlement_days,
face_amount,
fixed_bond_schedule,
[coupon_rate],
ActualActual(Bond),
Unadjusted,
redemption,
issue_date
)
pricing_engine = DiscountingBondEngine(self.ts)
bond.set_pricing_engine(pricing_engine)
self.assertAlmostEqual(bond.npv, 100.82127876105724)
quotes = [rh.quote for rh in self.rate_helpers]
delta, gamma = bucket_analysis(quotes, [bond])
self.assertEqual(len(quotes), len(delta))
old_values = [q.value for q in quotes]
delta_manual = []
gamma_manual = []
pv = bond.npv
shift = 1e-4
for v, q in zip(old_values, quotes):
q.value = v + shift
pv_plus = bond.npv
q.value = v - shift
pv_minus = bond.npv
delta_manual.append((pv_plus - pv_minus) * 0.5 / shift)
gamma_manual.append((pv_plus - 2 * pv + pv_minus) / shift ** 2)
q.value = v
assert_allclose(delta, delta_manual)
assert_allclose(gamma, gamma_manual, atol=1e-4)
def setUp(self):
self.calendar = TARGET()
self.settlement_days = 1
settlement_date = self.calendar.adjust(Date(28, January, 2011))
todays_date = self.calendar.advance(
settlement_date, -self.settlement_days, Days
)
Settings().evaluation_date = todays_date
depositData = [[ 1, Months, 4.581 ],
[ 2, Months, 4.573 ],
[ 3, Months, 4.557 ],
[ 6, Months, 4.496 ],
[ 9, Months, 4.490 ]]
swapData = [[ 1, Years, 4.54 ],
[ 5, Years, 4.99 ],
[ 10, Years, 5.47 ],
[ 20, Years, 5.89 ],
[ 30, Years, 5.96 ]]
self.rate_helpers = []
end_of_month = True
for m, period, rate in depositData:
tenor = Period(m, Months)
helper = DepositRateHelper(SimpleQuote(rate / 100),
tenor,
self.settlement_days,
self.calendar,
ModifiedFollowing,
end_of_month,
Actual360())
self.rate_helpers.append(helper)
liborIndex = USDLibor(Period(6, Months))
for m, period, rate in swapData:
sq_rate = SimpleQuote(rate/100)
helper = SwapRateHelper.from_tenor(
sq_rate, Period(m, Years), self.calendar, Annual, Unadjusted,
Thirty360(), liborIndex
)
self.rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
self.ts = PiecewiseYieldCurve(
BootstrapTrait.Discount, Interpolator.LogLinear, self.settlement_days,
self.calendar, self.rate_helpers, ts_day_counter, tolerance)
def _blsprice(spot,
strike,
risk_free_rate,
time,
volatility,
option_type='Call',
dividend=0.0,
calc='price'):
"""
Black-Scholes option pricing model + greeks.
"""
_spot = SimpleQuote(spot)
daycounter = ActualActual(ISMA)
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), volatility,
daycounter)
process = BlackScholesMertonProcess(_spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
if calc == 'price':
res = option.npv
elif calc == 'delta':
res = option.delta
elif calc == 'gamma':
res = option.gamma
elif calc == 'theta':
res = option.theta
elif calc == 'rho':
res = option.rho
elif calc == 'vega':
res = option.vega
elif calc == 'lambda':
res = option.delta * spot / option.npv
else:
raise ValueError('calc type %s is unknown' % calc)
return res
def setUp(self):
self.settings = Settings()
daycounter = ActualActual()
interest_rate = .1
dividend_yield = .04
self.risk_free_ts = flat_rate(interest_rate, daycounter)
self.dividend_ts = flat_rate(dividend_yield, daycounter)
s0 = SimpleQuote(32.0)
# Heston model
v0 = 0.05
kappa = 5.0
theta = 0.05
sigma = 1.0e-4
rho = -0.5
self.heston_process = HestonProcess(self.risk_free_ts,
self.dividend_ts, s0, v0, kappa,
theta, sigma, rho,
PartialTruncation)
v0 = 0.05
ival = {
'v0': v0,
'kappa': 3.7,
'theta': v0,
'sigma': 1.0,
'rho': -.6,
'lambda': .1,
'nu': -.5,
'delta': 0.3
}
spot = SimpleQuote(1200)
self.bates_process = BatesProcess(self.risk_free_ts, self.dividend_ts,
spot, ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'],
ival['rho'], ival['lambda'],
ival['nu'], ival['delta'])
a = 0.376739
sigma = 0.0209
self.hullwhite_process = HullWhiteProcess(self.risk_free_ts, a, sigma)
def test_bond_schedule_anotherday(self):
'''Test date calculations and role of settings when evaluation date
set to arbitrary date.
This test is known to fail with boost 1.42.
'''
todays_date = Date(30, August, 2011)
settings = Settings()
settings.evaluation_date = todays_date
calendar = TARGET()
effective_date = Date(10, Jul, 2006)
termination_date = calendar.advance(
effective_date, 10, Years, convention=Unadjusted)
settlement_days = 3
face_amount = 100.0
coupon_rate = 0.05
redemption = 100.0
fixed_bond_schedule = Schedule.from_rule(
effective_date,
termination_date,
Period(Annual),
calendar,
ModifiedFollowing,
ModifiedFollowing,
Rule.Backward
)
issue_date = effective_date
bond = FixedRateBond(
settlement_days,
face_amount,
fixed_bond_schedule,
[coupon_rate],
ActualActual(ISMA),
Following,
redemption,
issue_date
)
self.assertEqual(
calendar.advance(todays_date, 3, Days), bond.settlement_date())
def test_relative_yieldcurve(self):
settings = Settings()
settings.evaluation_date = Date(6, 10, 2016)
# Market information
calendar = TARGET()
quotes = [0.0096, 0.0145, 0.0194]
tenors = [3, 6, 12]
deposit_day_counter = Actual365Fixed()
convention = ModifiedFollowing
end_of_month = True
fixing_days = 3
rate_helpers = [
DepositRateHelper(quote, Period(month,
Months), fixing_days, calendar,
convention, end_of_month, deposit_day_counter)
for quote, month in zip(quotes, tenors)
]
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts_relative = PiecewiseYieldCurve(BootstrapTrait.Discount,
Interpolator.LogLinear, 2, calendar,
rate_helpers, ts_day_counter,
tolerance)
self.assertEqual(
ts_relative.reference_date,
calendar.advance(settings.evaluation_date, period=Period(2, Days)))
settings.evaluation_date = Date(10, 10, 2016)
settlement_date = calendar.advance(settings.evaluation_date,
period=Period(2, Days))
self.assertEqual(ts_relative.reference_date, settlement_date)
ts_absolute = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlement_date,
rate_helpers, ts_day_counter, tolerance)
self.assertEqual(ts_absolute.data, ts_relative.data)
self.assertEqual(ts_absolute.dates, ts_relative.dates)
self.assertEqual(ts_absolute.times, ts_relative.times)
def make_term_structure(rates, dt_obs):
"""
rates is a dictionary-like structure with labels as keys
and rates (decimal) as values.
TODO: Make it more generic
"""
settlement_date = pydate_to_qldate(dt_obs)
rate_helpers = []
for label in rates.keys():
r = rates[label]
h = make_rate_helper(label, r, settlement_date)
rate_helpers.append(h)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve('discount', 'loglinear', settlement_date,
rate_helpers, ts_day_counter, tolerance)
return ts
def test_bump_yieldcurve(self):
settings = Settings()
settings.evaluation_date = Date(6, 10, 2016)
# Market information
calendar = TARGET()
quotes = [
SimpleQuote(0.0096),
SimpleQuote(0.0145),
SimpleQuote(0.0194)
]
tenors = [3, 6, 12]
deposit_day_counter = Actual365Fixed()
convention = ModifiedFollowing
end_of_month = True
fixing_days = 3
rate_helpers = [
DepositRateHelper(quote, Period(month,
Months), fixing_days, calendar,
convention, end_of_month, deposit_day_counter)
for quote, month in zip(quotes, tenors)
]
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve(BootstrapTrait.Discount,
Interpolator.LogLinear, 2, calendar,
rate_helpers, ts_day_counter, tolerance)
old_discount = ts.discount(ts.max_date)
# parallel shift of 1 bps
for rh in rate_helpers:
rh.quote += 1e-4
self.assertEqual([q.value for q in quotes],
[rh.quote for rh in rate_helpers])
new_discount = ts.discount(ts.max_date)
self.assertTrue(new_discount < old_discount)
def test_discount_curve(self):
settings = Settings()
settings.evaluation_date = Date(6, 10, 2016)
# Market information
calendar = TARGET()
quotes = [
SimpleQuote(0.0096),
SimpleQuote(0.0145),
SimpleQuote(0.0194)
]
tenors = [3, 6, 12]
deposit_day_counter = Actual365Fixed()
convention = ModifiedFollowing
end_of_month = True
fixing_days = 3
rate_helpers = [
DepositRateHelper(quote, Period(month,
Months), fixing_days, calendar,
convention, end_of_month, deposit_day_counter)
for quote, month in zip(quotes, tenors)
]
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve(BootstrapTrait.ForwardRate,
Interpolator.BackwardFlat, 2, calendar,
rate_helpers, ts_day_counter, tolerance)
dates = [rh.latest_date for rh in rate_helpers]
dfs = [ts.discount(d) for d in dates]
dates.insert(0, ts.reference_date)
dfs.insert(0, 1)
ts_discount = DiscountCurve(dates, dfs, ts_day_counter, calendar)
self.assertTrue(ts.discount(0.75), ts_discount.discount(0.75))
def test_yield(self):
rates_data = [('Libor1M', .01), ('Libor3M', .015), ('Libor6M', .017),
('Swap1Y', .02), ('Swap2Y', .03), ('Swap3Y', .04),
('Swap5Y', .05), ('Swap7Y', .06), ('Swap10Y', .07),
('Swap20Y', .08)]
settlement_date = pydate_to_qldate('01-Dec-2013')
rate_helpers = []
for label, rate in rates_data:
h = make_rate_helper(label, rate, settlement_date)
rate_helpers.append(h)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve('discount', 'loglinear', settlement_date,
rate_helpers, ts_day_counter, tolerance)
zc = zero_rate(ts, (200, 300), settlement_date)
# not a real test - just verify execution
self.assertAlmostEqual(zc[1][0], 0.0189, 2)
def test_bond_schedule_today(self):
'''Test date calculations and role of settings when evaluation date
set to current date.
'''
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
calendar = TARGET()
effective_date = Date(10, Jul, 2006)
termination_date = calendar.advance(effective_date,
10,
Years,
convention=Unadjusted)
settlement_days = 3
face_amount = 100.0
coupon_rate = 0.05
redemption = 100.0
fixed_bond_schedule = Schedule(effective_date, termination_date,
Period(Annual), calendar,
ModifiedFollowing, ModifiedFollowing,
Backward)
issue_date = effective_date
bond = FixedRateBond(settlement_days, face_amount,
fixed_bond_schedule, [coupon_rate],
ActualActual(ISMA), Following, redemption,
issue_date)
self.assertEquals(calendar.advance(todays_date, 3, Days),
bond.settlement_date())
def test_extrapolation(self):
rate_helpers = build_helpers()
settings = Settings()
calendar = TARGET()
# must be a business Days
dtObs = date(2007, 4, 27)
eval_date = calendar.adjust(pydate_to_qldate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
print('dt Obs: %s\ndt Eval: %s\ndt Settle: %s' %
(dtObs, eval_date, settlement_date))
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-2
ts = PiecewiseYieldCurve[BootstrapTrait.Discount,
LogLinear].from_reference_date(
settlement_date,
rate_helpers,
ts_day_counter,
accuracy=tolerance)
# max_date raises an exception without extrapolation...
self.assertFalse(ts.extrapolation)
with self.assertRaises(RuntimeError) as ctx:
ts.discount(ts.max_date + 1)
self.assertTrue(
str(ctx.exception) in (
"time (30.011) is past max curve time (30.0082)",
"1st iteration: failed at 2nd alive instrument"))
fixedLegFrequency = Annual
fixedLegTenor = Period(1,Years)
fixedLegAdjustment = Unadjusted
fixedLegDayCounter = Thirty360()
floatingLegFrequency = Semiannual
floatingLegTenor = Period(6,Months)
floatingLegAdjustment = ModifiedFollowing
swapHelpers = [ SwapRateHelper.from_tenor(swaps[(n,unit)],
Period(n,unit), calendar,
fixedLegFrequency, fixedLegAdjustment,
fixedLegDayCounter, Euribor6M())
for n, unit in swaps.keys() ]
### Curve building
ts_daycounter = ActualActual(ISDA)
# term-structure construction
helpers = depositHelpers + swapHelpers
depoSwapCurve = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlementDate, helpers, ts_daycounter
)
helpers = depositHelpers[:2] + futuresHelpers + swapHelpers[1:]
depoFuturesSwapCurve = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear,settlementDate, helpers, ts_daycounter
)
helpers = depositHelpers[:3] + fraHelpers + swapHelpers
depoFraSwapCurve = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlementDate, helpers, ts_daycounter
def test_zero_curve(self):
try:
settings = Settings()
calendar = TARGET()
# must be a business Days
dtObs = date(2007, 4, 27)
eval_date = calendar.adjust(pydate_to_qldate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days,
Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
print('dt Obs: %s\ndt Eval: %s\ndt Settle: %s' %
(dtObs, eval_date, settlement_date))
depositData = [[1, Months, 'Libor1M', 5.32],
[3, Months, 'Libor3M', 5.35],
[6, Months, 'Libor6M', 5.35]]
swapData = [[1, Years, 'Swap1Y', 5.31], [2, Years, 'Swap2Y', 5.06],
[3, Years, 'Swap3Y', 5.00], [4, Years, 'Swap4Y', 5.01],
[5, Years, 'Swap5Y', 5.04], [7, Years, 'Swap7Y', 5.12],
[10, Years, 'Swap10Y', 5.22],
[30, Years, 'Swap30Y', 5.44]]
rate_helpers = []
end_of_month = True
for m, period, label, rate in depositData:
tenor = Period(m, Months)
helper = DepositRateHelper(SimpleQuote(rate / 100.0), tenor,
settlement_days, calendar,
ModifiedFollowing, end_of_month,
Actual360())
rate_helpers.append(helper)
liborIndex = Libor('USD Libor', Period(3, Months), settlement_days,
USDCurrency(), calendar, Actual360())
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, label, rate in swapData:
helper = SwapRateHelper.from_tenor(SimpleQuote(rate / 100.0),
Period(m, Years), calendar,
Semiannual,
ModifiedFollowing,
Thirty360(), liborIndex,
spread, fwdStart)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-2
ts = PiecewiseYieldCurve('discount', 'loglinear', settlement_date,
rate_helpers, ts_day_counter, tolerance)
# max_date raises an exception...
dtMax = ts.max_date
print('max date: %s' % dtMax)
except RuntimeError as e:
print('Exception (expected):\n%s' % e)
self.assertTrue(True)
except Exception:
self.assertFalse()
# <codecell>
def flat_rate(forward, daycounter):
return FlatForward(
forward=SimpleQuote(forward),
settlement_days=0,
calendar=NullCalendar(),
daycounter=daycounter
)
settings = Settings.instance()
settlement_date = today()
settings.evaluation_date = settlement_date
daycounter = ActualActual()
calendar = NullCalendar()
interest_rate = .1
dividend_yield = .04
risk_free_ts = flat_rate(interest_rate, daycounter)
dividend_ts = flat_rate(dividend_yield, daycounter)
s0 = SimpleQuote(100.0)
# Heston model
v0 = 0.05
kappa = 5.0
theta = 0.05
def test_deposit_swap(self):
settings = Settings()
# Market information
calendar = TARGET()
todays_date = Date(1, Mar, 2012)
# must be a business day
eval_date = calendar.adjust(todays_date)
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date);
depositData = [[ 1, Months, 4.581 ],
[ 2, Months, 4.573 ],
[ 3, Months, 4.557 ],
[ 6, Months, 4.496 ],
[ 9, Months, 4.490 ]]
swapData = [[ 1, Years, 4.54 ],
[ 5, Years, 4.99 ],
[ 10, Years, 5.47 ],
[ 20, Years, 5.89 ],
[ 30, Years, 5.96 ]]
rate_helpers = []
end_of_month = True
for m, period, rate in depositData:
tenor = Period(m, Months)
helper = DepositRateHelper(SimpleQuote(rate/100), tenor, settlement_days,
calendar, ModifiedFollowing, end_of_month,
Actual360())
rate_helpers.append(helper)
liborIndex = Libor(
'USD Libor', Period(6, Months), settlement_days, USDCurrency(),
calendar, Actual360()
)
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, rate in swapData:
helper = SwapRateHelper.from_tenor(
SimpleQuote(rate/100), Period(m, Years), calendar, Annual, Unadjusted, Thirty360(), liborIndex,
spread, fwdStart
)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlement_date, rate_helpers,
ts_day_counter, tolerance
)
self.assertEqual(settlement_date, ts.reference_date)
# this is not a real test ...
self.assertAlmostEqual(0.9103,
ts.discount(calendar.advance(todays_date, 2, Years)),3)
self.assertAlmostEqual(0.7836,
ts.discount(calendar.advance(todays_date, 5, Years)),3)
self.assertAlmostEqual(0.5827,
ts.discount(calendar.advance(todays_date, 10, Years)),3)
self.assertAlmostEqual(0.4223,
ts.discount(calendar.advance(todays_date, 15, Years)),3)
def test_display(self):
settings = Settings()
# Date setup
calendar = TARGET()
# Settlement date
settlement_date = calendar.adjust(Date(28, January, 2011))
# Evaluation date
fixing_days = 1
settlement_days = 1
todays_date = calendar.advance(
settlement_date, -fixing_days, Days
)
settings.evaluation_date = todays_date
# Bound attributes
face_amount = 100.0
redemption = 100.0
issue_date = Date(27, January, 2011)
maturity_date = Date(31, August, 2020)
coupon_rate = 0.03625
bond_yield = 0.034921
flat_discounting_term_structure = YieldTermStructure()
flat_term_structure = FlatForward(
reference_date = settlement_date,
forward = bond_yield,
daycounter = Actual365Fixed(), #actual_actual.ActualActual(actual_actual.Bond),
compounding = Compounded,
frequency = Semiannual)
# have a look at the FixedRateBondHelper to simplify this
# construction
flat_discounting_term_structure.link_to(flat_term_structure)
#Rate
fixed_bond_schedule = Schedule(
issue_date,
maturity_date,
Period(Semiannual),
UnitedStates(market=GOVERNMENTBOND),
Unadjusted,
Unadjusted,
Backward,
False);
bond = FixedRateBond(
settlement_days,
face_amount,
fixed_bond_schedule,
[coupon_rate],
ActualActual(Bond),
Unadjusted,
redemption,
issue_date
)
d=bf.startDate(bond)
zspd=bf.zSpread(bond, 100.0, flat_term_structure, Actual365Fixed(),
Compounded, Semiannual, settlement_date, 1e-6, 100, 0.5)
#Also need a test case for a PiecewiseTermStructure...
depositData = [[ 1, Months, 4.581 ],
[ 2, Months, 4.573 ],
[ 3, Months, 4.557 ],
[ 6, Months, 4.496 ],
[ 9, Months, 4.490 ]]
swapData = [[ 1, Years, 4.54 ],
[ 5, Years, 4.99 ],
[ 10, Years, 5.47 ],
[ 20, Years, 5.89 ],
[ 30, Years, 5.96 ]]
rate_helpers = []
end_of_month = True
for m, period, rate in depositData:
tenor = Period(m, Months)
helper = DepositRateHelper(SimpleQuote(rate/100), tenor, settlement_days,
calendar, ModifiedFollowing, end_of_month,
Actual360())
rate_helpers.append(helper)
liborIndex = Libor('USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360(),
YieldTermStructure(relinkable=False))
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, rate in swapData:
helper = SwapRateHelper.from_tenor(
SimpleQuote(rate/100), Period(m, Years), calendar, Annual, Unadjusted, Thirty360(), liborIndex,
spread, fwdStart
)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlement_date, rate_helpers,
ts_day_counter, tolerance)
pyc_zspd=bf.zSpread(bond, 102.0, ts, ActualActual(ISDA),
Compounded, Semiannual, Date(1, April, 2015), 1e-6, 100, 0.5)
pyc_zspd_disco=bf.zSpread(bond, 95.0, ts, ActualActual(ISDA),
Compounded, Semiannual, settlement_date, 1e-6, 100, 0.5)
yld = bf.yld(bond, 102.0, ActualActual(ISDA), Compounded, Semiannual, settlement_date, 1e-6, 100, 0.5)
dur = bf.duration(bond, yld, ActualActual(ISDA), Compounded, Semiannual, 2, settlement_date)
yld_disco = bf.yld(bond, 95.0, ActualActual(ISDA), Compounded, Semiannual, settlement_date, 1e-6, 100, 0.5)
dur_disco = bf.duration(bond, yld_disco, ActualActual(ISDA), Compounded, Semiannual, 2, settlement_date)
self.assertEqual(round(zspd, 6), 0.001281)
self.assertEqual(round(pyc_zspd, 4), -0.0264)
self.assertEqual(round(pyc_zspd_disco, 4), -0.0114)
self.assertEqual(round(yld, 4), 0.0338)
self.assertEqual(round(yld_disco, 4), 0.0426)
self.assertEqual(round(dur, 4), 8.0655)
self.assertEqual(round(dur_disco, 4), 7.9702)
def test_bates_det_jump(self):
# this looks like a bug in QL:
# Bates Det Jump model does not have sigma as parameter, yet
# changing sigma changes the result!
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 1290)
exercise = EuropeanExercise(exercise_date)
option = VanillaOption(payoff, exercise)
risk_free_ts = flat_rate(0.02, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
spot = 1290
ival = {'delta': 3.6828677022272715e-06,
'kappa': 19.02581428347027,
'kappaLambda': 1.1209758060939223,
'lambda': 0.06524550732595163,
'nu': -1.8968106563601956,
'rho': -0.7480898462264719,
'sigma': 1.0206363887835108,
'theta': 0.01965384459461113,
'thetaLambda': 0.028915397380738218,
'v0': 0.06566800935242285}
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_1 = option.net_present_value
ival['sigma'] = 1.e-6
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_2 = option.net_present_value
if(abs(calc_1-calc_2) > 1.e-5):
print('calc 1 %f calc 2 %f' % (calc_1, calc_2))
self.assertNotEqual(calc_1, calc_2)
def get_term_structure(df_libor, dtObs):
settings = Settings()
# libor as fixed in London, but cash-flows are determined according to
# US calendar, hence the need to combine both holidays lists
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dateToDate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
depositData = [[1, Months, 'Libor1M'], [3, Months, 'Libor3M'],
[6, Months, 'Libor6M']]
swapData = [[1, Years, 'Swap1Y'], [2, Years,
'Swap2Y'], [3, Years, 'Swap3Y'],
[4, Years, 'Swap4Y'], [5, Years, 'Swap5Y'],
[7, Years, 'Swap7Y'], [10, Years, 'Swap10Y'],
[30, Years, 'Swap30Y']]
rate_helpers = []
end_of_month = True
for m, period, label in depositData:
tenor = Period(m, Months)
rate = df_libor.get_value(dtObs, label)
helper = DepositRateHelper(float(rate / 100), tenor, settlement_days,
calendar, ModifiedFollowing, end_of_month,
Actual360())
rate_helpers.append(helper)
endOfMonth = True
liborIndex = Libor('USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360())
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, label in swapData:
rate = df_libor.get_value(dtObs, label)
helper = SwapRateHelper.from_tenor(rate / 100., Period(m, Years),
calendar, Annual, Unadjusted,
Thirty360(), liborIndex, spread,
fwdStart)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = term_structure_factory('discount', 'loglinear', settlement_date,
rate_helpers, ts_day_counter, tolerance)
return ts
def test_bucketanalysis_bond(self):
settings = Settings()
calendar = TARGET()
settlement_date = calendar.adjust(Date(28, January, 2011))
simple_quotes = []
fixing_days = 1
settlement_days = 1
todays_date = calendar.advance(settlement_date, -fixing_days, Days)
settings.evaluation_date = todays_date
face_amount = 100.0
redemption = 100.0
issue_date = Date(27, January, 2011)
maturity_date = Date(1, January, 2021)
coupon_rate = 0.055
bond_yield = 0.034921
flat_discounting_term_structure = YieldTermStructure()
flat_term_structure = FlatForward(reference_date=settlement_date,
forward=bond_yield,
daycounter=Actual365Fixed(),
compounding=Compounded,
frequency=Semiannual)
flat_discounting_term_structure.link_to(flat_term_structure)
fixed_bond_schedule = Schedule.from_rule(
issue_date, maturity_date, Period(Semiannual),
UnitedStates(market=GovernmentBond), Unadjusted, Unadjusted,
Backward, False)
bond = FixedRateBond(settlement_days, face_amount,
fixed_bond_schedule, [coupon_rate],
ActualActual(Bond), Unadjusted, redemption,
issue_date)
zspd = bf.zSpread(bond, 100.0, flat_term_structure, Actual365Fixed(),
Compounded, Semiannual, settlement_date, 1e-6, 100,
0.5)
depositData = [[1, Months, 4.581], [2, Months, 4.573],
[3, Months, 4.557], [6, Months, 4.496],
[9, Months, 4.490]]
swapData = [[1, Years, 4.54], [5, Years, 4.99], [10, Years, 5.47],
[20, Years, 5.89], [30, Years, 5.96]]
rate_helpers = []
end_of_month = True
for m, period, rate in depositData:
tenor = Period(m, Months)
sq_rate = SimpleQuote(rate / 100)
helper = DepositRateHelper(sq_rate, tenor, settlement_days,
calendar, ModifiedFollowing,
end_of_month, Actual360())
simple_quotes.append(sq_rate)
rate_helpers.append(helper)
liborIndex = Libor('USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360())
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, rate in swapData:
sq_rate = SimpleQuote(rate / 100)
helper = SwapRateHelper.from_tenor(sq_rate, Period(m, Years),
calendar, Annual, Unadjusted,
Thirty360(), liborIndex, spread,
fwdStart)
simple_quotes.append(sq_rate)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = PiecewiseYieldCurve.from_reference_date(BootstrapTrait.Discount,
Interpolator.LogLinear,
settlement_date,
rate_helpers,
ts_day_counter, tolerance)
discounting_term_structure = YieldTermStructure()
discounting_term_structure.link_to(ts)
pricing_engine = DiscountingBondEngine(discounting_term_structure)
bond.set_pricing_engine(pricing_engine)
self.assertAlmostEqual(bond.npv, 100.83702940160767)
ba = bucket_analysis([simple_quotes], [bond], [1], 0.0001, 1)
self.assertTrue(2, ba)
self.assertTrue(type(tuple), ba)
self.assertEqual(len(simple_quotes), len(ba[0][0]))
self.assertEqual(0, ba[0][0][8])
def get_term_structure(df_libor, dtObs):
settings = Settings()
# Market information
calendar = TARGET()
# must be a business day
eval_date = calendar.adjust(dateToDate(dtObs))
settings.evaluation_date = eval_date
settlement_days = 2
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date);
depositData =[[1, Months, 'Libor1M'],
[3, Months, 'Libor3M'],
[6, Months, 'Libor6M']]
swapData = [[ 1, Years, 'Swap1Y'],
[ 2, Years, 'Swap2Y'],
[ 3, Years, 'Swap3Y'],
[ 4, Years, 'Swap4Y'],
[ 5, Years, 'Swap5Y'],
[ 7, Years, 'Swap7Y'],
[ 10, Years,'Swap10Y'],
[ 30, Years,'Swap30Y']]
rate_helpers = []
end_of_month = True
for m, period, label in depositData:
tenor = Period(m, Months)
rate = df_libor.get_value(dtObs, label)
helper = DepositRateHelper(float(rate/100), tenor,
settlement_days,
calendar, ModifiedFollowing,
end_of_month,
Actual360())
rate_helpers.append(helper)
endOfMonth = True
liborIndex = Libor('USD Libor', Period(6, Months),
settlement_days,
USDCurrency(), calendar,
ModifiedFollowing,
endOfMonth, Actual360())
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
for m, period, label in swapData:
rate = df_libor.get_value(dtObs, label)
helper = SwapRateHelper(SimpleQuote(rate/100),
Period(m, Years),
calendar, Annual,
Unadjusted, Thirty360(),
liborIndex, spread, fwdStart)
rate_helpers.append(helper)
ts_day_counter = ActualActual(ISDA)
tolerance = 1.0e-15
ts = term_structure_factory('discount', 'loglinear',
settlement_date, rate_helpers,
ts_day_counter, tolerance)
return ts
def setUp(self):
self.calendar = UnitedKingdom()
today = Date(25, 11, 2009)
evaluation_date = self.calendar.adjust(today)
Settings().evaluation_date = evaluation_date
day_counter = ActualActual()
rpi_schedule = Schedule.from_rule(Date(20, 7,
2007), Date(20, 11, 2009),
Period(1, Months), self.calendar,
ModifiedFollowing)
self.cpi_ts = ZeroInflationTermStructure()
self.yts = FlatForward(evaluation_date, 0.05, day_counter)
self.ii = UKRPI(False, self.cpi_ts)
fix_data = [
206.1, 207.3, 208.0, 208.9, 209.7, 210.9, 209.8, 211.4, 212.1,
214.0, 215.1, 216.8, 216.5, 217.2, 218.4, 217.7, 216, 212.9, 210.1,
211.4, 211.3, 211.5, 212.8, 213.4, 213.4, 213.4, 214.4
]
for date, data in zip(rpi_schedule, fix_data):
self.ii.add_fixing(date, data)
dates = [
Date(25, 11, 2010),
Date(25, 11, 2011),
Date(26, 11, 2012),
Date(25, 11, 2013),
Date(25, 11, 2014),
Date(25, 11, 2015),
Date(25, 11, 2016),
Date(25, 11, 2017),
Date(25, 11, 2018),
Date(25, 11, 2019),
Date(25, 11, 2021),
Date(25, 11, 2024),
Date(26, 11, 2029),
Date(27, 11, 2034),
Date(25, 11, 2039),
Date(25, 11, 2049),
Date(25, 11, 2059)
]
rates = [
3.0495, 2.93, 2.9795, 3.029, 3.1425, 3.211, 3.2675, 3.3625, 3.405,
3.48, 3.576, 3.649, 3.751, 3.77225, 3.77, 3.734, 3.714
]
observation_lag = Period('2M')
self.helpers = [ZeroCouponInflationSwapHelper(
SimpleQuote(r / 100),
observation_lag,
maturity, self.calendar, ModifiedFollowing, day_counter, self.ii, self.yts) \
for maturity, r in zip(dates, rates)]
base_zero_rate = rates[0] / 100
self.cpi_ts.link_to(
PiecewiseZeroInflationCurve(Interpolator.Linear, evaluation_date,
self.calendar, day_counter,
observation_lag, self.ii.frequency,
self.ii.interpolated, base_zero_rate,
self.helpers))
