def dividendOption():
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++ General Parameter for all the computation +++++++++++++++++++++++
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# declaration of the today's date (date where the records are done)
todaysDate = Date(24, Jan, 2012) # INPUT
Settings.instance(
).evaluation_date = todaysDate #!\ IMPORTANT COMMAND REQUIRED FOR ALL VALUATIONS
calendar = UnitedStates() # INPUT
settlement_days = 2 # INPUT
# Calcul of the settlement date : need to add a period of 2 days to the todays date
settlementDate = calendar.advance(todaysDate,
period=Period(settlement_days, Days))
dayCounter = Actual360() # INPUT
currency = USDCurrency() # INPUT
print("Date of the evaluation: ", todaysDate)
print("Calendar used: ", calendar.name())
print("Number of settlement Days: ", settlement_days)
print("Date of settlement: ", settlementDate)
print("Convention of day counter: ", dayCounter.name())
print("Currency of the actual context:\t\t", currency.name)
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++ Description of the underlying +++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
underlying_name = "IBM"
underlying_price = 191.75 # INPUT
underlying_vol = 0.2094 # INPUT
print("**********************************")
print("Name of the underlying: ", underlying_name)
print("Price of the underlying at t0: ", underlying_price)
print("Volatility of the underlying: ", underlying_vol)
# For a great managing of price and vol objects --> Handle
underlying_priceH = SimpleQuote(underlying_price)
# We suppose the vol constant : his term structure is flat --> BlackConstantVol object
flatVolTS = BlackConstantVol(settlementDate, calendar, underlying_vol,
dayCounter)
# ++++++++++++++++++++ Description of Yield Term Structure
# Libor data record
print("**********************************")
print("Description of the Libor used for the Yield Curve construction")
Libor_dayCounter = Actual360()
liborRates = []
liborRatesTenor = []
# INPUT : all the following data are input : the rate and the corresponding tenor
# You could make the choice of more or less data
# --> However you have tho choice the instruments with different maturities
liborRates = [
0.002763, 0.004082, 0.005601, 0.006390, 0.007125, 0.007928, 0.009446,
0.01110
]
liborRatesTenor = [
Period(tenor, Months) for tenor in [1, 2, 3, 4, 5, 6, 9, 12]
]
for tenor, rate in zip(liborRatesTenor, liborRates):
print(tenor, "\t\t\t", rate)
# Swap data record
# description of the fixed leg of the swap
Swap_fixedLegTenor = Period(12, Months) # INPUT
Swap_fixedLegConvention = ModifiedFollowing # INPUT
Swap_fixedLegDayCounter = Actual360() # INPUT
# description of the float leg of the swap
Swap_iborIndex = Libor("USDLibor", Period(3, Months), settlement_days,
USDCurrency(), UnitedStates(), Actual360())
print("Description of the Swap used for the Yield Curve construction")
print("Tenor of the fixed leg: ", Swap_fixedLegTenor)
print("Index of the floated leg: ", Swap_iborIndex.name)
print("Maturity Rate ")
swapRates = []
swapRatesTenor = []
# INPUT : all the following data are input : the rate and the corresponding tenor
# You could make the choice of more or less data
# --> However you have tho choice the instruments with different maturities
swapRates = [
0.005681, 0.006970, 0.009310, 0.012010, 0.014628, 0.016881, 0.018745,
0.020260, 0.021545
]
swapRatesTenor = [Period(i, Years) for i in range(2, 11)]
for tenor, rate in zip(swapRatesTenor, swapRates):
print(tenor, "\t\t\t", rate)
# ++++++++++++++++++++ Creation of the vector of RateHelper (need for the Yield Curve construction)
# ++++++++++++++++++++ Libor
LiborFamilyName = currency.name + "Libor"
instruments = []
for rate, tenor in zip(liborRates, liborRatesTenor):
# Index description ___ creation of a Libor index
liborIndex = Libor(LiborFamilyName, tenor, settlement_days, currency,
calendar, Libor_dayCounter)
# Initialize rate helper ___ the DepositRateHelper link the recording rate with the Libor index
instruments.append(DepositRateHelper(rate, index=liborIndex))
# +++++++++++++++++++++ Swap
SwapFamilyName = currency.name + "swapIndex"
for tenor, rate in zip(swapRatesTenor, swapRates):
# swap description ___ creation of a swap index. The floating leg is described in the index 'Swap_iborIndex'
swapIndex = SwapIndex(SwapFamilyName, tenor, settlement_days, currency,
calendar, Swap_fixedLegTenor,
Swap_fixedLegConvention, Swap_fixedLegDayCounter,
Swap_iborIndex)
# Initialize rate helper __ the SwapRateHelper links the swap index width his rate
instruments.append(SwapRateHelper.from_index(rate, swapIndex))
# ++++++++++++++++++ Now the creation of the yield curve
riskFreeTS = PiecewiseYieldCurve('zero', 'linear', settlementDate,
instruments, dayCounter)
# ++++++++++++++++++ build of the underlying process : with a Black-Scholes model
print('Creating process')
bsProcess = BlackScholesProcess(underlying_priceH, riskFreeTS, flatVolTS)
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++ Description of the option +++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Option_name = "IBM Option"
maturity = Date(26, Jan, 2013)
strike = 190
option_type = 'call'
# Here, as an implementation exemple, we make the test with borth american and european exercise
europeanExercise = EuropeanExercise(maturity)
# The emericanExercise need also the settlement date, as his right to exerce the buy or call start at the settlement date!
#americanExercise = AmericanExercise(settlementDate, maturity)
americanExercise = AmericanExercise(maturity, settlementDate)
print("**********************************")
print("Description of the option: ", Option_name)
print("Date of maturity: ", maturity)
print("Type of the option: ", option_type)
print("Strike of the option: ", strike)
# ++++++++++++++++++ Description of the discrete dividends
# INPUT You have to determine the frequece and rates of the discrete dividend. Here is a sollution, but she's not the only one.
# Last know dividend:
dividend = 0.75 #//0.75
next_dividend_date = Date(10, Feb, 2012)
# HERE we have make the assumption that the dividend will grow with the quarterly croissance:
dividendCroissance = 1.03
dividendfrequence = Period(3, Months)
dividendDates = []
dividends = []
d = next_dividend_date
while d <= maturity:
dividendDates.append(d)
dividends.append(dividend)
d = d + dividendfrequence
dividend *= dividendCroissance
print("Discrete dividends ")
print("Dates Dividends ")
for date, div in zip(dividendDates, dividends):
print(date, " ", div)
# ++++++++++++++++++ Description of the final payoff
payoff = PlainVanillaPayoff(option_type, strike)
# ++++++++++++++++++ The OPTIONS : (American and European) with their dividends description:
dividendEuropeanOption = DividendVanillaOption(payoff, europeanExercise,
dividendDates, dividends)
dividendAmericanOption = DividendVanillaOption(payoff, americanExercise,
dividendDates, dividends)
# just too test
europeanOption = VanillaOption(payoff, europeanExercise)
americanOption = VanillaOption(payoff, americanExercise)
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++ Description of the pricing +++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# For the european options we have a closed analytic formula: The Black Scholes:
dividendEuropeanEngine = AnalyticDividendEuropeanEngine(bsProcess)
# For the american option we have make the choice of the finite difference model with the CrankNicolson scheme
# this model need to precise the time and space step
# More they are greater, more the calul will be precise.
americanGirdPoints = 600
americanTimeSteps = 600
dividendAmericanEngine = FDDividendAmericanEngine('CrankNicolson',
bsProcess,
americanTimeSteps,
americanGirdPoints)
# just to test
europeanEngine = AnalyticEuropeanEngine(bsProcess)
americanEngine = FDAmericanEngine('CrankNicolson', bsProcess,
americanTimeSteps, americanGirdPoints)
# ++++++++++++++++++++ Valorisation ++++++++++++++++++++++++++++++++++++++++
# Link the pricing Engine to the option
dividendEuropeanOption.set_pricing_engine(dividendEuropeanEngine)
dividendAmericanOption.set_pricing_engine(dividendAmericanEngine)
# just to test
europeanOption.set_pricing_engine(europeanEngine)
americanOption.set_pricing_engine(americanEngine)
# Now we make all the needing calcul
# ... and final results
print(
"NPV of the European Option with discrete dividends=0: {:.4f}".format(
dividendEuropeanOption.npv))
print("NPV of the European Option without dividend: {:.4f}".format(
europeanOption.npv))
print(
"NPV of the American Option with discrete dividends=0: {:.4f}".format(
dividendAmericanOption.npv))
print("NPV of the American Option without dividend: {:.4f}".format(
americanOption.npv))
# just a single test
print("ZeroRate with a maturity at ", maturity, ": ", \
riskFreeTS.zero_rate(maturity, dayCounter, Simple))
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(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
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('discount', '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.assertEquals(round(zspd, 6), 0.001281)
self.assertEquals(round(pyc_zspd, 4), -0.0264)
self.assertEquals(round(pyc_zspd_disco, 4), -0.0114)
self.assertEquals(round(yld, 4), 0.0338)
self.assertEquals(round(yld_disco, 4), 0.0426)
self.assertEquals(round(dur, 4), 8.0655)
self.assertEquals(round(dur_disco, 4), 7.9702)
def setUp(self):
self.day_counter = Actual360()
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()
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 / 100.0), 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 / 100.0),
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_swap_QL(self):
"""
Test that a swap with fixed coupon = fair rate has an NPV=0
Create from QL objects
"""
swap_type = Payer
nominal = 100.0
fixedConvention = Unadjusted
floatingConvention = ModifiedFollowing
fixedFrequency = Annual
floatingFrequency = Semiannual
fixedDayCount = Thirty360()
floatDayCount = Thirty360()
calendar = TARGET()
settlement_days = 2
eval_date = Date(02, 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,
Forward, False)
floatSchedule = Schedule(settlement_date, maturity,
Period(floatingFrequency),
calendar, floatingConvention,
floatingConvention,
Forward, False)
swap = VanillaSwap(swap_type, nominal, fixedSchedule, fixedRate,
fixedDayCount,
floatSchedule, index, floatingSpread,
floatDayCount, fixedConvention)
engine = DiscountingSwapEngine(termStructure,
False,
settlement_date, settlement_date)
swap.set_pricing_engine(engine)
l = swap.leg(0)
print l.to_str()
print 'Start date of swap ', swap.start_date
l = swap.leg(1)
print l.to_str()
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.assertAlmostEquals(p, 0)
class CreditDefaultSwapTest(unittest.TestCase):
calendar = TARGET()
today_date = today()
Settings().evaluation_date = today_date
hazard_rate = SimpleQuote(0.01234)
probability_curve = FlatHazardRate(0, calendar, hazard_rate, Actual360())
discount_curve = FlatForward(today_date, 0.06, Actual360())
issue_date = today_date
#calendar.advance(today_date, -1, Years)
maturity = calendar.advance(issue_date, 10, Years)
convention = Following
schedule = Schedule(issue_date, maturity, Period("3M"), calendar, convention,
convention, TwentiethIMM)
recovery_rate = 0.4
engine = MidPointCdsEngine(probability_curve, recovery_rate, discount_curve, True)
def test_fair_spread(self):
fixed_rate = 0.001
day_count = Actual360()
notional = 10000
cds = CreditDefaultSwap(SELLER, notional, fixed_rate, self.schedule,
self.convention, day_count, True, True)
cds.set_pricing_engine(self.engine)
fair_rate = cds.fair_spread
fair_cds = CreditDefaultSwap(SELLER, notional, fair_rate, self.schedule,
self.convention, day_count, True, True)
fair_cds.set_pricing_engine(self.engine)
self.assertAlmostEqual(fair_cds.npv, 0.)
def test_fair_upfront(self):
fixed_rate = 0.05
upfront = 0.001
day_count = Actual360()
notional = 10000
cds = CreditDefaultSwap.from_upfront(SELLER, notional, upfront, fixed_rate,
self.schedule,
self.convention, day_count, True, True)
cds.set_pricing_engine(self.engine)
fair_upfront = cds.fair_upfront
fair_cds = CreditDefaultSwap.from_upfront(SELLER, notional, fair_upfront,
fixed_rate, self.schedule,
self.convention, day_count, True, True)
fair_cds.set_pricing_engine(self.engine)
self.assertAlmostEqual(fair_cds.npv, 0.)
# same with null upfront
upfront = 0.
cds2 = CreditDefaultSwap.from_upfront(SELLER, notional, upfront,
fixed_rate, self.schedule,
self.convention, day_count, True, True)
cds2.set_pricing_engine(self.engine)
fair_upfront2 = cds.fair_upfront
fair_cds2 = CreditDefaultSwap.from_upfront(SELLER, notional, fair_upfront,
fixed_rate, self.schedule,
self.convention, day_count, True, True)
fair_cds2.set_pricing_engine(self.engine)
self.assertAlmostEqual(fair_cds2.npv, 0.)
def example02():
print("example 2:\n")
todays_date = Date(25, 9, 2014)
Settings.instance().evaluation_date = todays_date
calendar = TARGET()
term_date = calendar.adjust(todays_date + Period(2, Years), Following)
cds_schedule = Schedule(todays_date,
term_date,
Period(Quarterly),
WeekendsOnly(),
ModifiedFollowing,
ModifiedFollowing,
date_generation_rule=Rule.CDS)
for date in cds_schedule:
print(date)
print()
todays_date = Date(21, 10, 2014)
Settings.instance().evaluation_date = todays_date
quotes = [0.00006, 0.00045, 0.00081, 0.001840, 0.00256, 0.00337]
tenors = [1, 2, 3, 6, 9, 12]
deps = [
DepositRateHelper(q, Period(t, Months), 2, calendar, ModifiedFollowing,
False, Actual360()) for q, t in zip(quotes, tenors)
]
tenors = [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 20, 30]
quotes = [
0.00223, 0.002760, 0.003530, 0.004520, 0.005720, 0.007050, 0.008420,
0.009720, 0.010900, 0.012870, 0.014970, 0.017, 0.01821
]
swaps = [
SwapRateHelper.from_tenor(q, Period(t, Years), calendar, Annual,
ModifiedFollowing, Thirty360(), Euribor6M(),
SimpleQuote(0))
for q, t in zip(quotes, tenors)
]
helpers = deps + swaps
YC = PiecewiseYieldCurve.from_reference_date(BootstrapTrait.Discount,
Interpolator.LogLinear,
todays_date, helpers,
Actual365Fixed())
YC.extrapolation = True
print("ISDA rate curve:")
for h in helpers:
print("{0}: {1:.6f}\t{2:.6f}".format(
h.latest_date,
YC.zero_rate(h.latest_date, Actual365Fixed(), 2).rate,
YC.discount(h.latest_date)))
defaultTs0 = FlatHazardRate(0, WeekendsOnly(), 0.016739207493630,
Actual365Fixed())
cds_schedule = Schedule.from_rule(Date(22, 9, 2014), Date(20, 12, 2019),
Period(3, Months), WeekendsOnly(),
Following, Unadjusted, Rule.CDS, False)
nominal = 100000000
trade = CreditDefaultSwap(Side.Buyer, nominal, 0.01, cds_schedule,
Following, Actual360(), True, True,
Date(22, 10, 2014), Actual360(True), True)
engine = IsdaCdsEngine(defaultTs0, 0.4, YC, False)
trade.set_pricing_engine(engine)
print("reference trade NPV = {0}\n".format(trade.npv))
# convert them to Quote objects
#for n,unit in deposits.keys():
# deposits[(n,unit)] = SimpleQuote(deposits[(n,unit)])
for n, m in FRAs.keys():
FRAs[(n, m)] = SimpleQuote(FRAs[(n, m)])
for d in futures.keys():
futures[d] = SimpleQuote(futures[d])
for s in swaps.keys():
swaps[s] = SimpleQuote(swaps[s])
#for n,unit in swaps.keys():
# swaps[(n,unit)] = SimpleQuote(swaps[(n,unit)])
# build rate helpers
day_counter = Actual360()
settlementDays = 2
depositHelpers = [
DepositRateHelper(deposits[(n, unit)], Period(n, unit), settlementDays,
calendar, ModifiedFollowing, False, day_counter)
for n, unit in [(1,
Weeks), (1,
Months), (3,
Months), (6,
Months), (9,
Months), (1,
Years)]
]
day_counter = Actual360()
settlementDays = 2
def test_black_calibration(self):
# calibrate a Heston model to a constant volatility surface without
# smile. expected result is a vanishing volatility of the volatility.
# In addition theta and v0 should be equal to the constant variance
todays_date = today()
self.settings.evaluation_date = todays_date
daycounter = Actual360()
calendar = NullCalendar()
risk_free_ts = flat_rate(0.04, daycounter)
dividend_ts = flat_rate(0.50, daycounter)
option_maturities = [
Period(1, Months),
Period(2, Months),
Period(3, Months),
Period(6, Months),
Period(9, Months),
Period(1, Years),
Period(2, Years)
]
options = []
s0 = SimpleQuote(1.0)
vol = SimpleQuote(0.1)
volatility = vol.value
for maturity in option_maturities:
for moneyness in np.arange(-1.0, 2.0, 1.):
tau = daycounter.year_fraction(
risk_free_ts.reference_date,
calendar.advance(risk_free_ts.reference_date,
period=maturity))
forward_price = s0.value * dividend_ts.discount(tau) / \
risk_free_ts.discount(tau)
strike_price = forward_price * np.exp(
-moneyness * volatility * np.sqrt(tau))
options.append(
HestonModelHelper(maturity, calendar, s0.value,
strike_price, vol, risk_free_ts,
dividend_ts))
for sigma in np.arange(0.1, 0.7, 0.2):
v0 = 0.01
kappa = 0.2
theta = 0.02
rho = -0.75
process = HestonProcess(risk_free_ts, dividend_ts, s0, v0, kappa,
theta, sigma, rho)
self.assertEquals(v0, process.v0)
self.assertEquals(kappa, process.kappa)
self.assertEquals(theta, process.theta)
self.assertEquals(sigma, process.sigma)
self.assertEquals(rho, process.rho)
self.assertEquals(1.0, process.s0().value)
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 96)
for option in options:
option.set_pricing_engine(engine)
optimisation_method = LevenbergMarquardt(1e-8, 1e-8, 1e-8)
end_criteria = EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8)
model.calibrate(options, optimisation_method, end_criteria)
tolerance = 3.0e-3
self.assertFalse(model.sigma > tolerance)
self.assertAlmostEqual(model.kappa * model.theta,
model.kappa * volatility**2,
delta=tolerance)
self.assertAlmostEqual(model.v0, volatility**2, delta=tolerance)
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(Date.from_datetime(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.from_reference_date(BootstrapTrait.Discount,
Interpolator.LogLinear,
settlement_date, rate_helpers,
ts_day_counter, tolerance)
ts.extrapolation = True
return ts
def test_zero_curve_on_swap_index(self):
todays_date = today()
calendar = UnitedStates() # INPUT
dayCounter = Actual360() # INPUT
currency = USDCurrency() # INPUT
Settings.instance().evaluation_date = todays_date
settlement_days = 2
settlement_date = calendar.advance(todays_date,
period=Period(
settlement_days, Days))
liborRates = [
SimpleQuote(0.002763),
SimpleQuote(0.004082),
SimpleQuote(0.005601),
SimpleQuote(0.006390),
SimpleQuote(0.007125),
SimpleQuote(0.007928),
SimpleQuote(0.009446),
SimpleQuote(0.01110)
]
liborRatesTenor = [
Period(tenor, Months) for tenor in [1, 2, 3, 4, 5, 6, 9, 12]
]
Libor_dayCounter = Actual360()
swapRates = [
SimpleQuote(0.005681),
SimpleQuote(0.006970),
SimpleQuote(0.009310),
SimpleQuote(0.012010),
SimpleQuote(0.014628),
SimpleQuote(0.016881),
SimpleQuote(0.018745),
SimpleQuote(0.020260),
SimpleQuote(0.021545)
]
swapRatesTenor = [Period(i, Years) for i in range(2, 11)]
# description of the fixed leg of the swap
Swap_fixedLegTenor = Period(12, Months) # INPUT
Swap_fixedLegConvention = ModifiedFollowing # INPUT
Swap_fixedLegDayCounter = Actual360() # INPUT
# description of the float leg of the swap
Swap_iborIndex = Libor("USDLibor", Period(3, Months), settlement_days,
USDCurrency(), UnitedStates(), Actual360())
SwapFamilyName = currency.name + "swapIndex"
instruments = []
# ++++++++++++++++++++ Creation of the vector of RateHelper (need for the Yield Curve construction)
# ++++++++++++++++++++ Libor
LiborFamilyName = currency.name + "Libor"
instruments = []
for rate, tenor in zip(liborRates, liborRatesTenor):
# Index description ___ creation of a Libor index
liborIndex = Libor(LiborFamilyName, tenor, settlement_days,
currency, calendar, Libor_dayCounter)
# Initialize rate helper
# the DepositRateHelper link the recording rate with the Libor
# index
instruments.append(DepositRateHelper(rate, index=liborIndex))
for tenor, rate in zip(swapRatesTenor, swapRates):
# swap description ___ creation of a swap index. The floating leg is described in the index 'Swap_iborIndex'
swapIndex = SwapIndex(SwapFamilyName, tenor, settlement_days,
currency, calendar, Swap_fixedLegTenor,
Swap_fixedLegConvention,
Swap_fixedLegDayCounter, Swap_iborIndex)
# Initialize rate helper __ the SwapRateHelper links the swap index width his rate
instruments.append(SwapRateHelper.from_index(rate, swapIndex))
# ++++++++++++++++++ Now the creation of the yield curve
tolerance = 1.0e-15
ts = PiecewiseYieldCurve('zero', 'linear', settlement_date,
instruments, dayCounter, tolerance)
self.assertEqual(settlement_date, ts.reference_date)
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('discount', '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)
(10,Years): 0.05165,
(15,Years): 0.055175 }
# convert them to Quote objects
for n,unit in deposits.keys():
deposits[(n,unit)] = SimpleQuote(deposits[(n,unit)])
for n,m in FRAs.keys():
FRAs[(n,m)] = SimpleQuote(FRAs[(n,m)])
for d in futures.keys():
futures[d] = SimpleQuote(futures[d])
for n,unit in swaps.keys():
swaps[(n,unit)] = SimpleQuote(swaps[(n,unit)])
# build rate helpers
dayCounter = Actual360()
settlementDays = 2
depositHelpers = [ DepositRateHelper(deposits[(n,unit)],
Period(n,unit), settlementDays,
calendar, ModifiedFollowing,
False, dayCounter)
for n, unit in [(1,Weeks),(1,Months),(3,Months),
(6,Months),(9,Months),(1,Years)] ]
dayCounter = Actual360()
settlementDays = 2
fraHelpers = [ FraRateHelper(FRAs[(n,m)],
n, m, settlementDays,
calendar, ModifiedFollowing,
False, dayCounter)
for n, m in FRAs.keys() ]
def test_coupon_pricing(self):
tol = 1e-6
cms10y = EuriborSwapIsdaFixA(Period(10, Years), self.yts)
cms2y = EuriborSwapIsdaFixA(Period(2, Years), self.yts)
cms10y2y = SwapSpreadIndex("cms10y2y", cms10y, cms2y)
value_date = cms10y2y.value_date(self.ref_date)
pay_date = value_date + Period(1, Years)
cpn1a = CmsCoupon(pay_date, 10000., value_date, pay_date,
cms10y.fixing_days, cms10y, 1., 0., Date(), Date(),
Actual360(), False)
cpn1b = CmsCoupon(pay_date, 10000., value_date, pay_date,
cms2y.fixing_days, cms2y, 1., 0., Date(), Date(),
Actual360(), False)
cpn1 = CmsSpreadCoupon(pay_date, 10000., value_date, pay_date,
cms10y2y.fixing_days, cms10y2y, 1., 0., Date(),
Date(), Actual360(), False)
cpn1a.set_pricer(self.cms_pricer_ln)
cpn1b.set_pricer(self.cms_pricer_ln)
cpn1.set_pricer(self.cms_spread_pricer_ln)
self.assertEqual(cpn1.rate, cpn1a.rate - cpn1b.rate)
cms10y.add_fixing(self.ref_date, 0.05)
self.assertEqual(cpn1.rate, cpn1a.rate - cpn1b.rate)
cms2y.add_fixing(self.ref_date, 0.03)
self.assertEqual(cpn1.rate, cpn1a.rate - cpn1b.rate)
cpn2a = CmsCoupon(Date(23, 2, 2029), 10000., Date(23, 2, 2028),
Date(23, 2, 2029), 2, cms10y, 1., 0., Date(), Date(),
Actual360(), False)
cpn2b = CmsCoupon(Date(23, 2, 2029), 10000., Date(23, 2, 2028),
Date(23, 2, 2029), 2, cms2y, 1., 0., Date(), Date(),
Actual360(), False)
plain_cpn = CappedFlooredCmsSpreadCoupon(Date(23, 2, 2029),
10000.,
Date(23, 2, 2028),
Date(23, 2, 2029),
2,
cms10y2y,
1.,
0.,
day_counter=Actual360())
capped_cpn = CappedFlooredCmsSpreadCoupon(Date(23, 2, 2029),
10000.,
Date(23, 2, 2028),
Date(23, 2, 2029),
2,
cms10y2y,
1.,
0.,
0.03,
day_counter=Actual360())
floored_cpn = CappedFlooredCmsSpreadCoupon(Date(23, 2, 2029),
10000.,
Date(23, 2, 2028),
Date(23, 2, 2029),
2,
cms10y2y,
1.,
0.,
QL_NULL_REAL,
0.01,
day_counter=Actual360())
collared_cpn = CappedFlooredCmsSpreadCoupon(Date(23, 2, 2029),
10000.,
Date(23, 2, 2028),
Date(23, 2, 2029),
2,
cms10y2y,
1.,
0.,
0.03,
0.01,
day_counter=Actual360())
cpn2a.set_pricer(self.cms_pricer_ln)
cpn2b.set_pricer(self.cms_pricer_ln)
plain_cpn.set_pricer(self.cms_spread_pricer_ln)
capped_cpn.set_pricer(self.cms_spread_pricer_ln)
floored_cpn.set_pricer(self.cms_spread_pricer_ln)
collared_cpn.set_pricer(self.cms_spread_pricer_ln)
r = self.mc_reference_value(cpn2a, cpn2b, self.swLn,
self.correlation.value)
self.assertAlmostEqual(r.mean(), plain_cpn.rate)
self.assertAlmostEqual(
np.clip(r, None, 0.03).mean(), capped_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, None).mean(), floored_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, 0.03).mean(), collared_cpn.rate, 5)
cpn2a.set_pricer(self.cms_pricer_sln)
cpn2b.set_pricer(self.cms_pricer_sln)
plain_cpn.set_pricer(self.cms_spread_pricer_sln)
capped_cpn.set_pricer(self.cms_spread_pricer_sln)
floored_cpn.set_pricer(self.cms_spread_pricer_sln)
collared_cpn.set_pricer(self.cms_spread_pricer_sln)
r = self.mc_reference_value(cpn2a, cpn2b, self.swSLn,
self.correlation.value)
self.assertAlmostEqual(r.mean(), plain_cpn.rate)
self.assertAlmostEqual(
np.clip(r, None, 0.03).mean(), capped_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, None).mean(), floored_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, 0.03).mean(), collared_cpn.rate, 5)
cpn2a.set_pricer(self.cms_pricer_n)
cpn2b.set_pricer(self.cms_pricer_n)
plain_cpn.set_pricer(self.cms_spread_pricer_n)
capped_cpn.set_pricer(self.cms_spread_pricer_n)
floored_cpn.set_pricer(self.cms_spread_pricer_n)
collared_cpn.set_pricer(self.cms_spread_pricer_n)
r = self.mc_reference_value(cpn2a, cpn2b, self.swN,
self.correlation.value)
self.assertAlmostEqual(r.mean(), plain_cpn.rate)
self.assertAlmostEqual(
np.clip(r, None, 0.03).mean(), capped_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, None).mean(), floored_cpn.rate, 5)
self.assertAlmostEqual(
np.clip(r, 0.01, 0.03).mean(), collared_cpn.rate, 5)
