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('discount', '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 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 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.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"))
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.value += 1e-4
self.assertEqual([q.value for q in quotes], [rh.quote.value for rh in rate_helpers])
new_discount = ts.discount(ts.max_date)
self.assertTrue(new_discount < old_discount)
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)
def bootstrap_term_structure(self, interpolator=Interpolator.LogLinear):
tolerance = 1.0e-15
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = self._eval_date
settings.evaluation_date = eval_date
settlement_days = self._params.settlement_days
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
ts = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount,
interpolator,
settlement_date,
self._rate_helpers,
DayCounter.from_name(self._termstructure_daycount),
tolerance,
)
self._term_structure = ts
self._discount_term_structure = YieldTermStructure()
self._discount_term_structure.link_to(ts)
self._forecast_term_structure = YieldTermStructure()
self._forecast_term_structure.link_to(ts)
return ts
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('discount',
'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('discount',
'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 bootstrap_term_structure(self, interpolator=LogLinear):
tolerance = 1.0e-15
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = self._eval_date
settings.evaluation_date = eval_date
settlement_days = self._params.settlement_days
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
ts = PiecewiseYieldCurve[BootstrapTrait.Discount,
interpolator].from_reference_date(
settlement_date,
self._rate_helpers,
DayCounter.from_name(
self._termstructure_daycount),
accuracy=tolerance)
self._term_structure = ts
self._discount_term_structure = YieldTermStructure()
self._discount_term_structure.link_to(ts)
self._forecast_term_structure = YieldTermStructure()
self._forecast_term_structure.link_to(ts)
return ts
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, 6)
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.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"))
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 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 zbt_libor_yield(instruments,
yields,
pricing_date,
basis='Actual/Actual (Bond)',
compounding_freq='Continuous',
maturity_dates=None):
"""
Bootstrap a zero-coupon curve from libor rates and swap yields
Args:
instruments: list of instruments, of the form Libor?M for Libor rates
and Swap?Y for swap rates
yields: market rates
pricing_date: the date where market data is observed. Settlement
is by default 2 days after pricing_date
Optional:
compounding_frequency: ... of zero-coupon rates. By default:
'Continuous'
Returns:
zero_rate: zero-coupon rate
maturity_date: ... of corresponding rate
"""
calendar = TARGET()
settings = Settings()
# must be a business day
eval_date = calendar.adjust(pydate_to_qldate(pricing_date))
settings.evaluation_date = eval_date
rates = dict(zip(instruments, yields))
ts = make_term_structure(rates, pricing_date)
cnt = DayCounter.from_name(basis)
if maturity_dates is None:
# schedule of maturity dates from settlement date to last date on
# the term structure
s = Schedule(effective_date=ts.reference_date,
termination_date=ts.max_date,
tenor=Period(1, Months),
calendar=TARGET())
maturity_dates = [qldate_to_pydate(dt) for dt in s.dates()]
cp_freq = Compounding[compounding_freq]
zc = [
ts.zero_rate(pydate_to_qldate(dt),
day_counter=cnt,
compounding=cp_freq).rate for dt in maturity_dates
]
return (maturity_dates, zc)
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_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 _set_evaluation_date(self, dt_obs):
if(~isinstance(dt_obs, Date)):
dt_obs = pydate_to_qldate(dt_obs)
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dt_obs)
settings.evaluation_date = eval_date
self._eval_date = eval_date
return eval_date
def _cfamounts(coupon_rate, pricing_date, maturity_date,
period, basis):
"""
cash flow schedule
"""
_period = str_to_frequency(period)
evaluation_date = pydate_to_qldate(pricing_date)
settings = Settings()
settings.evaluation_date = evaluation_date
calendar = TARGET()
termination_date = pydate_to_qldate(maturity_date)
# effective date must be before settlement date, but do not
# care about exact issuance date of bond
effective_date = Date(termination_date.day, termination_date.month,
evaluation_date.year)
effective_date = calendar.advance(
effective_date, -1, Years, convention=Unadjusted)
face_amount = 100.0
redemption = 100.0
fixed_bond_schedule = Schedule(
effective_date,
termination_date,
Period(_period),
calendar,
ModifiedFollowing,
ModifiedFollowing,
Backward
)
issue_date = effective_date
cnt = DayCounter.from_name(basis)
settlement_days = 2
bond = FixedRateBond(
settlement_days,
face_amount,
fixed_bond_schedule,
[coupon_rate],
cnt,
Following,
redemption,
issue_date)
res = zip(*bond.cashflows)
return(res)
def zbt_libor_yield(instruments, yields, pricing_date,
basis='Actual/Actual (Bond)',
compounding_freq='Continuous',
maturity_dates=None):
"""
Bootstrap a zero-coupon curve from libor rates and swap yields
Args:
insruments: list of instruments, of the form Libor?M for Libor rates
and Swap?Y for swap rates
yields: market rates
pricing_date: the date where market data is observed. Settlement
is by default 2 days after pricing_date
Optional:
compounding_frequency: ... of zero-coupon rates. By default:
'Continuous'
Returns:
zero_rate: zero-coupon rate
maturity_date: ... of corresponding rate
"""
calendar = TARGET()
settings = Settings()
# must be a business day
eval_date = calendar.adjust(pydate_to_qldate(pricing_date))
settings.evaluation_date = eval_date
rates = dict(zip(instruments, yields))
ts = make_term_structure(rates, pricing_date)
cnt = DayCounter.from_name(basis)
if maturity_dates is None:
# schedule of maturity dates from settlement date to last date on
# the term structure
s = Schedule(effective_date=ts.reference_date,
termination_date=ts.max_date,
tenor=Period(1, Months),
calendar=TARGET())
maturity_dates = [qldate_to_pydate(dt) for dt in s.dates()]
cp_freq = compounding_from_name(compounding_freq)
zc = [ts.zero_rate(date=pydate_to_qldate(dt),
day_counter=cnt,
compounding=cp_freq).rate for dt in maturity_dates]
return (maturity_dates, zc)
def test_excel_example_with_fixed_rate_bond(self):
"""Port the QuantLib Excel adding bond example to Python. """
todays_date = Date(25, 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(
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,
)
discounting_term_structure = YieldTermStructure(relinkable=True)
flat_term_structure = FlatForward(
settlement_days=1,
forward=0.044,
calendar=NullCalendar(),
daycounter=Actual365Fixed(),
compounding=Continuous,
frequency=Annual,
)
discounting_term_structure.link_to(flat_term_structure)
engine = DiscountingBondEngine(discounting_term_structure)
bond.set_pricing_engine(engine)
self.assertEquals(Date(10, Jul, 2016), termination_date)
self.assertEquals(calendar.advance(todays_date, 3, Days), bond.settlement_date())
self.assertEquals(Date(11, Jul, 2016), bond.maturity_date)
self.assertAlmostEqual(0.6849, bond.accrued_amount(bond.settlement_date()), 4)
self.assertAlmostEqual(102.1154, bond.clean_price, 4)
def _set_evaluation_date(self, dt_obs):
if not isinstance(dt_obs, Date):
dt_obs = pydate_to_qldate(dt_obs)
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dt_obs)
settings.evaluation_date = eval_date
self._eval_date = eval_date
return eval_date
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_excel_example_with_fixed_rate_bond(self):
'''Port the QuantLib Excel adding bond example to Python. '''
todays_date = Date(25, 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, Backward)
issue_date = effective_date
bond = FixedRateBond(settlement_days, face_amount,
fixed_bond_schedule, [coupon_rate],
ActualActual(ISMA), Following, redemption,
issue_date)
discounting_term_structure = YieldTermStructure()
flat_term_structure = FlatForward(settlement_days=1,
forward=0.044,
calendar=NullCalendar(),
daycounter=Actual365Fixed(),
compounding=Continuous,
frequency=Annual)
discounting_term_structure.link_to(flat_term_structure)
engine = DiscountingBondEngine(discounting_term_structure)
bond.set_pricing_engine(engine)
self.assertEqual(Date(10, Jul, 2016), termination_date)
self.assertEqual(calendar.advance(todays_date, 3, Days),
bond.settlement_date())
self.assertEqual(Date(11, Jul, 2016), bond.maturity_date)
self.assertAlmostEqual(0.6849,
bond.accrued_amount(bond.settlement_date()), 4)
self.assertAlmostEqual(102.1154, bond.clean_price, 4)
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_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.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlement_date, rate_helpers,
ts_day_counter, 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)
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 test_using_settings(self):
settings = Settings()
evaluation_date = today()
# have to set the evaluation date before the test as it is a global
# attribute for the whole library ... meaning that previous test_cases
# might have set this to another date
settings.evaluation_date = evaluation_date
self.assertEqual(settings.evaluation_date, evaluation_date)
self.assertTrue(settings.version.startswith('1'))
def test_using_settings(self):
settings = Settings()
evaluation_date = today()
# have to set the evaluation date before the test as it is a global
# attribute for the whole library ... meaning that previous test_cases
# might have set this to another date
settings.evaluation_date = evaluation_date
self.assertEqual(settings.evaluation_date, evaluation_date)
self.assertTrue(settings.version.startswith('1'))
def test_bucket_analysis_option(self):
settings = Settings()
calendar = TARGET()
todays_date = Date(15, May, 1998)
settlement_date = Date(17, May, 1998)
settings.evaluation_date = todays_date
option_type = Put
underlying = 40
strike = 40
dividend_yield = 0.00
risk_free_rate = 0.001
volatility = 0.20
maturity = Date(17, May, 1999)
daycounter = Actual365Fixed()
underlyingH = SimpleQuote(underlying)
payoff = PlainVanillaPayoff(option_type, strike)
flat_term_structure = FlatForward(reference_date=settlement_date,
forward=risk_free_rate,
daycounter=daycounter)
flat_dividend_ts = FlatForward(reference_date=settlement_date,
forward=dividend_yield,
daycounter=daycounter)
flat_vol_ts = BlackConstantVol(settlement_date, calendar, volatility,
daycounter)
black_scholes_merton_process = BlackScholesMertonProcess(
underlyingH, flat_dividend_ts, flat_term_structure, flat_vol_ts)
european_exercise = EuropeanExercise(maturity)
european_option = VanillaOption(payoff, european_exercise)
analytic_european_engine = AnalyticEuropeanEngine(
black_scholes_merton_process)
european_option.set_pricing_engine(analytic_european_engine)
ba_eo = bucket_analysis([[underlyingH]], [european_option], [1], 0.50,
1)
self.assertTrue(2, ba_eo)
self.assertTrue(type(tuple), ba_eo)
self.assertEqual(1, len(ba_eo[0][0]))
self.assertAlmostEqual(-0.4582666150152517, ba_eo[0][0][0])
def make_rate_helper(label, rate, dt_obs, currency='USD'):
"""
Wrapper for deposit and swaps rate helpers makers
For Swaps: assume USD swap fixed rates vs. 6M Libor
TODO: make this more general
"""
if(currency.upper() != 'USD'):
raise Exception("Only supported currency is USD.")
rate_type, tenor, period = _parse_rate_label(label)
if not isinstance(dt_obs, Date):
dt_obs = pydate_to_qldate(dt_obs)
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dt_obs)
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)
end_of_month = True
if((rate_type == 'SWAP') & (period == 'Y')):
liborIndex = Libor(
'USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360()
)
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
helper = SwapRateHelper.from_tenor(
SimpleQuote(rate),
Period(tenor, Years),
calendar, Annual,
Unadjusted, Thirty360(),
liborIndex, spread, fwdStart)
elif((rate_type == 'LIBOR') & (period == 'M')):
helper = DepositRateHelper(SimpleQuote(rate),
Period(tenor, Months),
settlement_days,
calendar,
ModifiedFollowing,
end_of_month,
Actual360())
else:
raise Exception("Rate type %s not supported" % label)
return (helper)
def test_bucket_analysis_option(self):
settings = Settings()
calendar = TARGET()
todays_date = Date(15, May, 1998)
settlement_date = Date(17, May, 1998)
settings.evaluation_date = todays_date
option_type = Put
underlying = 40
strike = 40
dividend_yield = 0.00
risk_free_rate = 0.001
volatility = SimpleQuote(0.20)
maturity = Date(17, May, 1999)
daycounter = Actual365Fixed()
underlyingH = SimpleQuote(underlying)
payoff = PlainVanillaPayoff(option_type, strike)
flat_term_structure = FlatForward(reference_date=settlement_date,
forward=risk_free_rate,
daycounter=daycounter)
flat_dividend_ts = FlatForward(reference_date=settlement_date,
forward=dividend_yield,
daycounter=daycounter)
flat_vol_ts = BlackConstantVol(settlement_date, calendar, volatility,
daycounter)
black_scholes_merton_process = BlackScholesMertonProcess(
underlyingH, flat_dividend_ts, flat_term_structure, flat_vol_ts)
european_exercise = EuropeanExercise(maturity)
european_option = VanillaOption(payoff, european_exercise)
analytic_european_engine = AnalyticEuropeanEngine(
black_scholes_merton_process)
european_option.set_pricing_engine(analytic_european_engine)
delta, gamma = bucket_analysis([underlyingH, volatility],
[european_option],
shift=1e-4,
type=Centered)
self.assertAlmostEqual(delta[0], european_option.delta)
self.assertAlmostEqual(delta[1], european_option.vega)
self.assertAlmostEqual(gamma[0], european_option.gamma, 5)
def heston_helpers(spot, df_option, dtTrade, df_rates):
"""
Create array of heston options helpers
"""
DtSettlement = dateToQLDate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
# convert data frame (date/value) into zero curve
# expect the index to be a date, and 1 column of values
risk_free_ts = dfToZeroCurve(df_rates['iRate'], dtTrade)
dividend_ts = dfToZeroCurve(df_rates['iDiv'], dtTrade)
# loop through rows in option data frame, construct
# helpers for bid/ask
oneDay = datetime.timedelta(days=1)
dtExpiry = [dtTrade + int(t*365)*oneDay for t in df_option['TTM']]
df_option['dtExpiry'] = dtExpiry
options = []
for index, row in df_option.T.iteritems():
strike = row['Strike']
if (strike/spot.value > 1.3) | (strike/spot.value < .7):
continue
days = int(365*row['TTM'])
maturity = Period(days, Days)
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['IVBid']),
risk_free_ts, dividend_ts,
ImpliedVolError))
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['IVAsk']),
risk_free_ts, dividend_ts,
ImpliedVolError))
return {'options':options, 'spot': spot}
def test_all_types_of_piecewise_curves(self):
settings = Settings()
# Market information
calendar = TARGET()
todays_date = Date(12, September, 2008)
# must be a business day
settings.evaluation_date = calendar.adjust(todays_date)
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 = []
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)
tolerance = 1.0e-15
for trait in BootstrapTrait:
for interpolation in Interpolator:
ts = PiecewiseYieldCurve.from_reference_date(
trait, interpolation, settlement_date, rate_helpers,
deposit_day_counter, tolerance)
self.assertIsNotNone(ts)
self.assertEqual(Date(18, September, 2008), ts.reference_date)
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_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_all_types_of_piecewise_curves(self):
settings = Settings()
# Market information
calendar = TARGET()
todays_date = Date(12, September, 2008)
# must be a business day
settings.evaluation_date = calendar.adjust(todays_date)
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 = []
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)
tolerance = 1.0e-15
for trait in VALID_TRAITS:
for interpolation in VALID_INTERPOLATORS:
ts = PiecewiseYieldCurve(
trait, interpolation, settlement_date, rate_helpers,
deposit_day_counter, tolerance
)
self.assertIsNotNone(ts)
self.assertEqual( Date(18, September, 2008), ts.reference_date)
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 make_rate_helper(label, rate, dt_obs, currency='USD'):
"""
Wrapper for deposit and swaps rate helpers makers
For Swaps: assume USD swap fixed rates vs. 6M Libor
TODO: make this more general
"""
if(currency.upper() != 'USD'):
raise Exception("Only supported currency is USD.")
rate_type, tenor, period = _parse_rate_label(label)
if not isinstance(dt_obs, Date):
dt_obs = pydate_to_qldate(dt_obs)
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dt_obs)
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)
end_of_month = True
if((rate_type == 'SWAP') & (period == 'Y')):
liborIndex = Libor(
'USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360()
)
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
helper = SwapRateHelper.from_tenor(rate,
Period(tenor, Years),
calendar, Annual,
Unadjusted, Thirty360(),
liborIndex, spread, fwdStart)
elif((rate_type == 'LIBOR') & (period == 'M')):
helper = DepositRateHelper(rate, Period(tenor, Months),
settlement_days,
calendar, ModifiedFollowing,
end_of_month,
Actual360())
else:
raise Exception("Rate type %s not supported" % label)
return (helper)
def set_quotes(self, dt_obs, quotes):
self._quotes = quotes
if(~isinstance(dt_obs, Date)):
dt_obs = pydate_to_qldate(dt_obs)
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = calendar.adjust(dt_obs)
settings.evaluation_date = eval_date
self._eval_date = eval_date
self._rate_helpers = []
for quote in quotes:
# construct rate helper
helper = make_rate_helper(self, quote, eval_date)
self._rate_helpers.append(helper)
def heston_pricer(trade_date, options, params, rates, spot):
"""
Price a list of European options with heston model.
"""
spot = SimpleQuote(spot)
risk_free_ts = df_to_zero_curve(rates[nm.INTEREST_RATE], trade_date)
dividend_ts = df_to_zero_curve(rates[nm.DIVIDEND_YIELD], trade_date)
process = HestonProcess(risk_free_ts, dividend_ts, spot, **params)
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
settlement_date = pydate_to_qldate(trade_date)
settings = Settings()
settings.evaluation_date = settlement_date
modeled_values = np.zeros(len(options))
for index, row in options.T.iteritems():
expiry_date = row[nm.EXPIRY_DATE]
strike = row[nm.STRIKE]
option_type = Call if row[nm.OPTION_TYPE] == nm.CALL_OPTION else Put
payoff = PlainVanillaPayoff(option_type, strike)
expiry_qldate = pydate_to_qldate(expiry_date)
exercise = EuropeanExercise(expiry_qldate)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(engine)
modeled_values[index] = option.net_present_value
prices = options.filter(
items=[nm.EXPIRY_DATE, nm.STRIKE, nm.OPTION_TYPE, nm.SPOT])
prices[nm.PRICE] = modeled_values
prices[nm.TRADE_DATE] = trade_date
return prices
def heston_pricer(trade_date, options, params, rates, spot):
"""
Price a list of European options with heston model.
"""
spot = SimpleQuote(spot)
risk_free_ts = df_to_zero_curve(rates[nm.INTEREST_RATE], trade_date)
dividend_ts = df_to_zero_curve(rates[nm.DIVIDEND_YIELD], trade_date)
process = HestonProcess(risk_free_ts, dividend_ts, spot, **params)
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
settlement_date = pydate_to_qldate(trade_date)
settings = Settings()
settings.evaluation_date = settlement_date
modeled_values = np.zeros(len(options))
for index, row in options.T.iteritems():
expiry_date = row[nm.EXPIRY_DATE]
strike = row[nm.STRIKE]
option_type = Call if row[nm.OPTION_TYPE] == nm.CALL_OPTION else Put
payoff = PlainVanillaPayoff(option_type, strike)
expiry_qldate = pydate_to_qldate(expiry_date)
exercise = EuropeanExercise(expiry_qldate)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(engine)
modeled_values[index] = option.net_present_value
prices = options.filter(items=[nm.EXPIRY_DATE, nm.STRIKE,
nm.OPTION_TYPE, nm.SPOT])
prices[nm.PRICE] = modeled_values
prices[nm.TRADE_DATE] = trade_date
return prices
def bootstrap_term_structure(self, interpolator='loglinear'):
tolerance = 1.0e-15
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = self._eval_date
settings.evaluation_date = eval_date
settlement_days = self._params.settlement_days
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
ts = PiecewiseYieldCurve(
'discount', interpolator, settlement_date, self._rate_helpers,
DayCounter.from_name(self._termstructure_daycount), tolerance)
self._term_structure = ts
self._discount_term_structure = YieldTermStructure(relinkable=True)
self._discount_term_structure.link_to(ts)
self._forecast_term_structure = YieldTermStructure(relinkable=True)
self._forecast_term_structure.link_to(ts)
return ts
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 bootstrap_term_structure(self):
tolerance = 1.0e-15
settings = Settings()
calendar = JointCalendar(UnitedStates(), UnitedKingdom())
# must be a business day
eval_date = self._eval_date
settings.evaluation_date = eval_date
settlement_days = self._params.settlement_days
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
ts = term_structure_factory(
'discount', 'loglinear',
settlement_date, self._rate_helpers,
DayCounter.from_name(self._termstructure_daycount),
tolerance)
self._term_structure = ts
self._discount_term_structure = YieldTermStructure(relinkable=True)
self._discount_term_structure.link_to(ts)
self._forecasting_term_structure = YieldTermStructure(relinkable=True)
self._forecasting_term_structure.link_to(ts)
return 0
def test_deposit_swap(self):
settings = Settings()
# Market information
calendar = TARGET()
# must be a business day
eval_date = calendar.adjust(today())
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(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:
rate = SimpleQuote(rate/100)
helper = SwapRateHelper(rate, 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)
# this is not a real test ...
self.assertAlmostEquals(0.9103,
ts.discount(calendar.advance(today(), 2, Years)),3)
self.assertAlmostEquals(0.7836,
ts.discount(calendar.advance(today(), 5, Years)),3)
self.assertAlmostEquals(0.5827,
ts.discount(calendar.advance(today(), 10, Years)),3)
self.assertAlmostEquals(0.4223,
ts.discount(calendar.advance(today(), 15, Years)),3)
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(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 in swapData:
rate = df_libor.get_value(dtObs, label)
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-15
ts = PiecewiseYieldCurve('discount',
'loglinear',
settlement_date,
rate_helpers,
ts_day_counter,
tolerance)
return ts
def _bndprice(bond_yield, coupon_rate, pricing_date, maturity_date, period,
basis, compounding_frequency):
"""
Clean price and accrued interest of a bond
"""
_period = str_to_frequency(period)
evaluation_date = pydate_to_qldate(pricing_date)
settings = Settings()
settings.evaluation_date = evaluation_date
calendar = TARGET()
termination_date = pydate_to_qldate(maturity_date)
# effective date must be before settlement date, but do not
# care about exact issuance date of bond
effective_date = Date(termination_date.day, termination_date.month,
evaluation_date.year)
effective_date = calendar.advance(effective_date,
-1,
Years,
convention=Unadjusted)
settlement_date = calendar.advance(evaluation_date,
2,
Days,
convention=ModifiedFollowing)
face_amount = 100.0
redemption = 100.0
fixed_bond_schedule = Schedule(effective_date, termination_date,
Period(_period), calendar,
ModifiedFollowing, ModifiedFollowing,
Backward)
issue_date = effective_date
cnt = DayCounter.from_name(basis)
settlement_days = 2
bond = FixedRateBond(settlement_days, face_amount, fixed_bond_schedule,
[coupon_rate], cnt, Following, redemption, issue_date)
discounting_term_structure = YieldTermStructure(relinkable=True)
cnt_yield = DayCounter.from_name('Actual/Actual (Historical)')
flat_term_structure = FlatForward(settlement_days=2,
forward=bond_yield,
calendar=NullCalendar(),
daycounter=cnt_yield,
compounding=Compounded,
frequency=_period)
discounting_term_structure.link_to(flat_term_structure)
engine = DiscountingBondEngine(discounting_term_structure)
bond.set_pricing_engine(engine)
price = bond.clean_price
ac = bond.accrued_amount(pydate_to_qldate(settlement_date))
return (price, ac)
def heston_helpers(df_option, dtTrade=None, df_rates=None, ival=None):
"""
Create array of heston options helpers
"""
if dtTrade is None:
dtTrade = df_option['dtTrade'][0]
DtSettlement = datetoQLDate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
if df_rates is None:
df_tmp = DataFrame.filter(df_option, items=['dtExpiry', 'IR', 'IDIV'])
grouped = df_tmp.groupby('dtExpiry')
df_rates = grouped.agg(lambda x: x[0])
# convert data frame (date/value) into zero curve
# expect the index to be a date, and 1 column of values
risk_free_ts = dfToZeroCurve(df_rates['R'], dtTrade)
dividend_ts = dfToZeroCurve(df_rates['D'], dtTrade)
# back out the spot from any forward
iRate = df_option['R'][0]
iDiv = df_option['D'][0]
TTM = df_option['T'][0]
Fwd = df_option['F'][0]
spot = SimpleQuote(Fwd*np.exp(-(iRate-iDiv)*TTM))
print('Spot: %f risk-free rate: %f div. yield: %f' % (spot.value, iRate, iDiv))
# loop through rows in option data frame, construct
# helpers for bid/ask
oneDay = datetime.timedelta(days=1)
dtExpiry = [dtTrade + int(t*365)*oneDay for t in df_option['T']]
df_option['dtExpiry'] = dtExpiry
options = []
for index, row in df_option.T.iteritems():
strike = row['K']
if (strike/spot.value > 1.3) | (strike/spot.value < .7):
continue
days = int(365*row['T'])
maturity = Period(days, Days)
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['VB']),
risk_free_ts, dividend_ts,
ImpliedVolError))
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['VA']),
risk_free_ts, dividend_ts,
ImpliedVolError))
return {'options':options, 'spot': spot}
def heston_helpers(df_option, dtTrade=None, df_rates=None, ival=None):
"""
Create array of heston options helpers
"""
if dtTrade is None:
dtTrade = df_option['dtTrade'][0]
DtSettlement = pydate_to_qldate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
if df_rates is None:
df_tmp = DataFrame.filter(df_option, items=['dtExpiry', 'IR', 'IDIV'])
grouped = df_tmp.groupby('dtExpiry')
df_rates = grouped.agg(lambda x: x[0])
# convert data frame (date/value) into zero curve
# expect the index to be a date, and 1 column of values
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
# back out the spot from any forward
iRate = df_option['R'][0]
iDiv = df_option['D'][0]
TTM = df_option['T'][0]
Fwd = df_option['F'][0]
spot = SimpleQuote(Fwd * np.exp(-(iRate - iDiv) * TTM))
print('Spot: %f risk-free rate: %f div. yield: %f' % \
(spot.value, iRate, iDiv))
# loop through rows in option data frame, construct
# helpers for bid/ask
oneDay = datetime.timedelta(days=1)
dtExpiry = [dtTrade + int(t * 365) * oneDay for t in df_option['T']]
df_option['dtExpiry'] = dtExpiry
options = []
for index, row in df_option.T.iteritems():
strike = row['K']
if (strike / spot.value > 1.3) | (strike / spot.value < .7):
continue
days = int(365 * row['T'])
maturity = Period(days, Days)
options.append(
HestonModelHelper(maturity, calendar, spot.value, strike,
SimpleQuote(row['VB']), risk_free_ts,
dividend_ts, ImpliedVolError))
options.append(
HestonModelHelper(maturity, calendar, spot.value, strike,
SimpleQuote(row['VA']), risk_free_ts,
dividend_ts, ImpliedVolError))
return {'options': options, 'spot': spot}
def test_pricing_bond():
'''Inspired by the C++ code from http://quantcorner.wordpress.com/.'''
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
discounting_term_structure = YieldTermStructure(relinkable=True)
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
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
)
bond.set_pricing_engine(discounting_term_structure)
return bond
def test_excel_example_with_floating_rate_bond(self):
todays_date = Date(25, 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_date = calendar.adjust(Date(28, January, 2011))
settlement_days = 3 #1
face_amount = 13749769.27 #2
coupon_rate = 0.05
redemption = 100.0
float_bond_schedule = Schedule(effective_date, termination_date,
Period(Annual), calendar,
ModifiedFollowing, ModifiedFollowing,
Backward) #3
flat_discounting_term_structure = YieldTermStructure(relinkable=True)
forecastTermStructure = YieldTermStructure(relinkable=True)
dc = Actual360()
ibor_index = Euribor6M(forecastTermStructure) #5
fixing_days = 2 #6
gearings = [1, 0.0] #7
spreads = [1, 0.05] #8
caps = [] #9
floors = [] #10
pmt_conv = ModifiedFollowing #11
issue_date = effective_date
float_bond = FloatingRateBond(settlement_days, face_amount,
float_bond_schedule, ibor_index, dc,
fixing_days, gearings, spreads, caps,
floors, pmt_conv, redemption, issue_date)
flat_term_structure = FlatForward(settlement_days=1,
forward=0.055,
calendar=NullCalendar(),
daycounter=Actual365Fixed(),
compounding=Continuous,
frequency=Annual)
flat_discounting_term_structure.link_to(flat_term_structure)
forecastTermStructure.link_to(flat_term_structure)
engine = DiscountingBondEngine(flat_discounting_term_structure)
float_bond.set_pricing_engine(engine)
cons_option_vol = ConstantOptionletVolatility(settlement_days,
UnitedStates(SETTLEMENT),
pmt_conv, 0.95,
Actual365Fixed())
coupon_pricer = BlackIborCouponPricer(cons_option_vol)
set_coupon_pricer(float_bond, coupon_pricer)
self.assertEquals(Date(10, Jul, 2016), termination_date)
self.assertEquals(calendar.advance(todays_date, 3, Days),
float_bond.settlement_date())
self.assertEquals(Date(11, Jul, 2016), float_bond.maturity_date)
self.assertAlmostEqual(
0.6944, float_bond.accrued_amount(float_bond.settlement_date()), 4)
self.assertAlmostEqual(98.2485, float_bond.dirty_price, 4)
self.assertAlmostEqual(13500805.2469, float_bond.npv, 4)
def test_pricing_bond(self):
'''Inspired by the C++ code from http://quantcorner.wordpress.com/.'''
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
discounting_term_structure = YieldTermStructure(relinkable=True)
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
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)
bond.set_pricing_engine(discounting_term_structure)
# tests
self.assertTrue(Date(27, January, 2011), bond.issue_date)
self.assertTrue(Date(31, August, 2020), bond.maturity_date)
self.assertTrue(settings.evaluation_date, bond.valuation_date)
# the following assertion fails but must be verified
self.assertAlmostEqual(101.1, bond.clean_price, 1)
self.assertAlmostEqual(101.1, bond.net_present_value, 1)
self.assertAlmostEqual(101.1, bond.dirty_price)
self.assertAlmostEqual(0.009851, bond.accrued_amount())
print(settings.evaluation_date)
print('Principal: {}'.format(face_amount))
print('Issuing date: {} '.format(bond.issue_date))
print('Maturity: {}'.format(bond.maturity_date))
print('Coupon rate: {:.4%}'.format(coupon_rate))
print('Yield: {:.4%}'.format(bond_yield))
print('Net present value: {:.4f}'.format(bond.net_present_value))
print('Clean price: {:.4f}'.format(bond.clean_price))
print('Dirty price: {:.4f}'.format(bond.dirty_price))
print('Accrued coupon: {:.6f}'.format(bond.accrued_amount()))
print('Accrued coupon: {:.6f}'.format(
bond.accrued_amount(Date(1, March, 2011))))
def test_pricing_bond(self):
'''Inspired by the C++ code from http://quantcorner.wordpress.com/.'''
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
discounting_term_structure = YieldTermStructure(relinkable=True)
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
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
)
bond.set_pricing_engine(discounting_term_structure)
# tests
self.assertTrue(Date(27, January, 2011), bond.issue_date)
self.assertTrue(Date(31, August, 2020), bond.maturity_date)
self.assertTrue(settings.evaluation_date, bond.valuation_date)
# the following assertion fails but must be verified
self.assertAlmostEqual(101.1, bond.clean_price, 1)
self.assertAlmostEqual(101.1, bond.net_present_value, 1)
self.assertAlmostEqual(101.1, bond.dirty_price)
self.assertAlmostEqual(0.009851, bond.accrued_amount())
print settings.evaluation_date
print 'Principal: {}'.format(face_amount)
print 'Issuing date: {} '.format(bond.issue_date)
print 'Maturity: {}'.format(bond.maturity_date)
print 'Coupon rate: {:.4%}'.format(coupon_rate)
print 'Yield: {:.4%}'.format(bond_yield)
print 'Net present value: {:.4f}'.format(bond.net_present_value)
print 'Clean price: {:.4f}'.format(bond.clean_price)
print 'Dirty price: {:.4f}'.format(bond.dirty_price)
print 'Accrued coupon: {:.6f}'.format(bond.accrued_amount())
print 'Accrued coupon: {:.6f}'.format(
bond.accrued_amount(Date(1, March, 2011))
)
def test_swap_from_market(self):
"""
Test that a swap with fixed coupon = fair rate has an NPV=0
Create from market
"""
eval_date = Date(2, January, 2014)
settings = Settings()
settings.evaluation_date = eval_date
calendar = TARGET()
settlement_date = calendar.advance(eval_date, 2, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
length = 5
fixed_rate = .05
floating_spread = 0.0
m = libor_market('USD(NY)')
quotes = [('DEP', '1W', SimpleQuote(0.0382)),
('DEP', '1M', SimpleQuote(0.0372)),
('DEP', '3M', SimpleQuote(0.0363)),
('DEP', '6M', SimpleQuote(0.0353)),
('DEP', '9M', SimpleQuote(0.0348)),
('DEP', '1Y', SimpleQuote(0.0345)),
('SWAP', '2Y', SimpleQuote(0.037125)),
('SWAP', '3Y', SimpleQuote(0.0398)),
('SWAP', '5Y', SimpleQuote(0.0443)),
('SWAP', '10Y', SimpleQuote(0.05165)),
('SWAP', '15Y', SimpleQuote(0.055175))]
m.set_quotes(eval_date, quotes)
m.bootstrap_term_structure()
dt = Date(2, January, 2015)
df = m.discount(dt)
print('discount factor for %s (USD Libor): %f' % (dt, df))
swap = m.create_fixed_float_swap(settlement_date, length, fixed_rate,
floating_spread)
fixed_l = swap.fixed_leg
float_l = swap.floating_leg
f = swap.fair_rate
print('fair rate: %f' % f)
p = swap.net_present_value
print('NPV: %f' % p)
fixed_npv = swap.fixed_leg_npv
float_npv = swap.floating_leg_npv
# verify calculation by discounting both legs
tot = 0.0
for frc in fixed_l:
df = m.discount(frc.date)
tot += frc.amount * df
print('fixed npv: %f discounted cf: %f' % (fixed_npv, tot))
self.assertAlmostEqual(fixed_npv, -tot)
tot = 0.0
for ic in float_l:
df = m.discount(ic.date)
tot += ic.amount * df
print('float npv: %f discounted cf: %f' % (float_npv, tot))
self.assertAlmostEqual(float_npv, tot)
def test_swap_QL(self):
"""
Test that a swap with fixed coupon = fair rate has an NPV=0
Create from QL objects
"""
nominal = 100.0
fixedConvention = Unadjusted
floatingConvention = ModifiedFollowing
fixedFrequency = Annual
floatingFrequency = Semiannual
fixedDayCount = Thirty360()
floatDayCount = Thirty360()
calendar = TARGET()
settlement_days = 2
eval_date = Date(2, January, 2014)
settings = Settings()
settings.evaluation_date = eval_date
settlement_date = calendar.advance(eval_date, settlement_days, Days)
# must be a business day
settlement_date = calendar.adjust(settlement_date)
termStructure = YieldTermStructure(relinkable=True)
termStructure.link_to(FlatForward(settlement_date, 0.05,
Actual365Fixed()))
index = Libor('USD Libor', Period(6, Months), settlement_days,
USDCurrency(), calendar, Actual360(),
termStructure)
length = 5
fixedRate = .05
floatingSpread = 0.0
maturity = calendar.advance(settlement_date, length, Years,
convention=floatingConvention)
fixedSchedule = Schedule(settlement_date, maturity,
Period(fixedFrequency),
calendar, fixedConvention, fixedConvention,
Rule.Forward, False)
floatSchedule = Schedule(settlement_date, maturity,
Period(floatingFrequency),
calendar, floatingConvention,
floatingConvention,
Rule.Forward, False)
engine = DiscountingSwapEngine(termStructure,
False,
settlement_date, settlement_date)
for swap_type in [Payer, Receiver]:
swap = VanillaSwap(swap_type, nominal, fixedSchedule, fixedRate,
fixedDayCount,
floatSchedule, index, floatingSpread,
floatDayCount, fixedConvention)
swap.set_pricing_engine(engine)
fixed_leg = swap.fixed_leg
floating_leg = swap.floating_leg
f = swap.fair_rate
print('fair rate: %f' % f)
p = swap.net_present_value
print('NPV: %f' % p)
swap = VanillaSwap(swap_type, nominal, fixedSchedule, f,
fixedDayCount,
floatSchedule, index, floatingSpread,
floatDayCount, fixedConvention)
swap.set_pricing_engine(engine)
p = swap.net_present_value
print('NPV: %f' % p)
self.assertAlmostEqual(p, 0)
def test_heston_hw_calibration(self):
"""
From Quantlib test suite
"""
print("Testing Heston Hull-White calibration...")
## Calibration of a hybrid Heston-Hull-White model using
## the finite difference HestonHullWhite pricing engine
## Input surface is based on a Heston-Hull-White model with
## Hull-White: a = 0.00883, \sigma = 0.00631
## Heston : \nu = 0.12, \kappa = 2.0,
## \theta = 0.09, \sigma = 0.5, \rho=-0.75
## Equity Short rate correlation: -0.5
dc = Actual365Fixed()
calendar = TARGET()
todays_date = Date(28, March, 2004)
settings = Settings()
settings.evaluation_date = todays_date
r_ts = flat_rate(todays_date, 0.05, dc)
## assuming, that the Hull-White process is already calibrated
## on a given set of pure interest rate calibration instruments.
hw_process = HullWhiteProcess(r_ts, a=0.00883, sigma=0.00631)
q_ts = flat_rate(todays_date, 0.02, dc)
s0 = SimpleQuote(100.0)
# vol surface
strikes = [50, 75, 90, 100, 110, 125, 150, 200]
maturities = [1 / 12., 3 / 12., 0.5, 1.0, 2.0, 3.0, 5.0, 7.5, 10]
vol = [
0.482627, 0.407617, 0.366682, 0.340110, 0.314266, 0.280241,
0.252471, 0.325552, 0.464811, 0.393336, 0.354664, 0.329758,
0.305668, 0.273563, 0.244024, 0.244886, 0.441864, 0.375618,
0.340464, 0.318249, 0.297127, 0.268839, 0.237972, 0.225553,
0.407506, 0.351125, 0.322571, 0.305173, 0.289034, 0.267361,
0.239315, 0.213761, 0.366761, 0.326166, 0.306764, 0.295279,
0.284765, 0.270592, 0.250702, 0.222928, 0.345671, 0.314748,
0.300259, 0.291744, 0.283971, 0.273475, 0.258503, 0.235683,
0.324512, 0.303631, 0.293981, 0.288338, 0.283193, 0.276248,
0.266271, 0.250506, 0.311278, 0.296340, 0.289481, 0.285482,
0.281840, 0.276924, 0.269856, 0.258609, 0.303219, 0.291534,
0.286187, 0.283073, 0.280239, 0.276414, 0.270926, 0.262173
]
start_v0 = 0.2 * 0.2
start_theta = start_v0
start_kappa = 0.5
start_sigma = 0.25
start_rho = -0.5
equityShortRateCorr = -0.5
corrConstraint = HestonHullWhiteCorrelationConstraint(
equityShortRateCorr)
heston_process = HestonProcess(r_ts, q_ts, s0, start_v0, start_kappa,
start_theta, start_sigma, start_rho)
h_model = HestonModel(heston_process)
h_engine = AnalyticHestonEngine(h_model)
options = []
# first calibrate a heston model to get good initial
# parameters
for i in range(len(maturities)):
maturity = Period(int(maturities[i] * 12.0 + 0.5), Months)
for j, s in enumerate(strikes):
v = SimpleQuote(vol[i * len(strikes) + j])
helper = HestonModelHelper(maturity, calendar, s0.value, s, v,
r_ts, q_ts, PriceError)
helper.set_pricing_engine(h_engine)
options.append(helper)
om = LevenbergMarquardt(1e-6, 1e-8, 1e-8)
# Heston model
h_model.calibrate(options, om,
EndCriteria(400, 40, 1.0e-8, 1.0e-4, 1.0e-8))
print("Heston calibration")
print("v0: %f" % h_model.v0)
print("theta: %f" % h_model.theta)
print("kappa: %f" % h_model.kappa)
print("sigma: %f" % h_model.sigma)
print("rho: %f" % h_model.rho)
h_process_2 = HestonProcess(r_ts, q_ts, s0, h_model.v0, h_model.kappa,
h_model.theta, h_model.sigma, h_model.rho)
hhw_model = HestonModel(h_process_2)
options = []
for i in range(len(maturities)):
tGrid = np.max((10.0, maturities[i] * 10.0))
hhw_engine = FdHestonHullWhiteVanillaEngine(
hhw_model, hw_process, equityShortRateCorr, tGrid, 61, 13, 9,
0, True, FdmSchemeDesc.Hundsdorfer())
hhw_engine.enable_multiple_strikes_caching(strikes)
maturity = Period(int(maturities[i] * 12.0 + 0.5), Months)
# multiple strikes engine works best if the first option
# per maturity has the average strike (because the first
# option is priced first during the calibration and
# the first pricing is used to calculate the prices
# for all strikes
# list of strikes by distance from moneyness
indx = np.argsort(np.abs(np.array(strikes) - s0.value))
for j, tmp in enumerate(indx):
js = indx[j]
s = strikes[js]
v = SimpleQuote(vol[i * len(strikes) + js])
helper = HestonModelHelper(maturity, calendar, s0.value,
strikes[js], v, r_ts, q_ts,
PriceError)
helper.set_pricing_engine(hhw_engine)
options.append(helper)
vm = LevenbergMarquardt(1e-6, 1e-2, 1e-2)
hhw_model.calibrate(options, vm,
EndCriteria(400, 40, 1.0e-8, 1.0e-4, 1.0e-8),
corrConstraint)
print("Heston HW calibration with FD engine")
print("v0: %f" % hhw_model.v0)
print("theta: %f" % hhw_model.theta)
print("kappa: %f" % hhw_model.kappa)
print("sigma: %f" % hhw_model.sigma)
print("rho: %f" % hhw_model.rho)
relTol = 0.05
expected_v0 = 0.12
expected_kappa = 2.0
expected_theta = 0.09
expected_sigma = 0.5
expected_rho = -0.75
self.assertAlmostEquals(np.abs(hhw_model.v0 - expected_v0) /
expected_v0,
0,
delta=relTol)
self.assertAlmostEquals(np.abs(hhw_model.theta - expected_theta) /
expected_theta,
0,
delta=relTol)
self.assertAlmostEquals(np.abs(hhw_model.kappa - expected_kappa) /
expected_kappa,
0,
delta=relTol)
self.assertAlmostEquals(np.abs(hhw_model.sigma - expected_sigma) /
expected_sigma,
0,
delta=relTol)
self.assertAlmostEquals(np.abs(hhw_model.rho - expected_rho) /
expected_rho,
0,
delta=relTol)
