def _blsimpv(price, spot, strike, risk_free_rate, time, option_type, dividend):
spot = SimpleQuote(spot)
daycounter = ActualActual(ISMA)
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), .3, daycounter)
process = BlackScholesMertonProcess(spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
accuracy = 0.001
max_evaluations = 1000
min_vol = 0.01
max_vol = 2
vol = option.implied_volatility(price, process, accuracy, max_evaluations,
min_vol, max_vol)
return vol
def test_smith(self):
# test against result published in
# Journal of Computational Finance Vol. 11/1 Fall 2007
# An almost exact simulation method for the heston model
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
timeToMaturity = 4
exercise_date = settlement_date + timeToMaturity * 365
c_payoff = PlainVanillaPayoff(Call, 100)
exercise = EuropeanExercise(exercise_date)
risk_free_ts = flat_rate(0., daycounter)
dividend_ts = flat_rate(0., daycounter)
s0 = SimpleQuote(100.0)
v0 = 0.0194
kappa = 1.0407
theta = 0.0586
sigma = 0.5196
rho = -.6747
nb_steps_a = 100
nb_paths = 20000
seed = 12347
process = HestonProcess(risk_free_ts, dividend_ts, s0, v0, kappa,
theta, sigma, rho, QUADRATICEXPONENTIAL)
model = HestonModel(process)
option = VanillaOption(c_payoff, exercise)
engine = AnalyticHestonEngine(model, 144)
option.set_pricing_engine(engine)
price_fft = option.net_present_value
engine = MCEuropeanHestonEngine(process,
antithetic_variate=True,
steps_per_year=nb_steps_a,
required_samples=nb_paths,
seed=seed)
option.set_pricing_engine(engine)
price_mc = option.net_present_value
expected = 15.1796
tolerance = .05
self.assertAlmostEqual(price_fft, expected, delta=tolerance)
self.assertAlmostEqual(price_mc, expected, delta=tolerance)
def test_european_vanilla_option_usage(self):
european_exercise = EuropeanExercise(self.maturity)
european_option = VanillaOption(self.payoff, european_exercise)
analytic_european_engine = AnalyticEuropeanEngine(
self.black_scholes_merton_process)
european_option.set_pricing_engine(analytic_european_engine)
self.assertAlmostEquals(3.844308, european_option.net_present_value, 6)
def test_analytic_versus_black(self):
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 30)
exercise = EuropeanExercise(exercise_date)
risk_free_ts = flat_rate(0.1, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
s0 = SimpleQuote(32.0)
v0 = 0.05
kappa = 5.0
theta = 0.05
sigma = 1.0e-4
rho = 0.0
process = HestonProcess(
risk_free_ts, dividend_ts, s0, v0, kappa, theta, sigma, rho
)
option = VanillaOption(payoff, exercise)
engine = AnalyticHestonEngine(HestonModel(process), 144)
option.set_pricing_engine(engine)
calculated = option.net_present_value
year_fraction = daycounter.year_fraction(
settlement_date, exercise_date
)
forward_price = 32 * np.exp((0.1 - 0.04) * year_fraction)
expected = blackFormula(
payoff.type, payoff.strike, forward_price,
np.sqrt(0.05 * year_fraction)
) * np.exp(-0.1 * year_fraction)
tolerance = 2.0e-7
self.assertAlmostEqual(
calculated,
expected,
delta=tolerance
)
def test_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 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 _blsprice(spot,
strike,
risk_free_rate,
time,
volatility,
option_type='Call',
dividend=0.0,
calc='price'):
"""
Black-Scholes option pricing model + greeks.
"""
_spot = SimpleQuote(spot)
daycounter = ActualActual(ISMA)
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), volatility,
daycounter)
process = BlackScholesMertonProcess(_spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
if calc == 'price':
res = option.npv
elif calc == 'delta':
res = option.delta
elif calc == 'gamma':
res = option.gamma
elif calc == 'theta':
res = option.theta
elif calc == 'rho':
res = option.rho
elif calc == 'vega':
res = option.vega
elif calc == 'lambda':
res = option.delta * spot / option.npv
else:
raise ValueError('calc type %s is unknown' % calc)
return res
def test_implied_volatility(self):
european_exercise = EuropeanExercise(self.maturity)
european_option = VanillaOption(self.payoff, european_exercise)
vol = SimpleQuote(.18)
proc = ImpliedVolatilityHelper.clone(self.black_scholes_merton_process,
vol)
analytic_european_engine = AnalyticEuropeanEngine(proc)
implied_volatility = ImpliedVolatilityHelper.calculate(
european_option, analytic_european_engine, vol, 3.844308, .001,
500, .1, .5)
self.assertAlmostEqual(.20, implied_volatility, 4)
def test_str(self):
quote_str = str(self.underlyingH)
self.assertEquals('Simple Quote: 36.000000', quote_str)
payoff_str = str(self.payoff)
self.assertEquals('Payoff: Vanilla Put @ 40.000000', payoff_str)
exercise = EuropeanExercise(self.maturity)
exercise_str = str(exercise)
self.assertEquals('Exercise type: European', exercise_str)
option = VanillaOption(self.payoff, exercise)
self.assertEquals('Exercise type: European', str(option.exercise))
vanilla_str = str(option)
self.assertEquals('VanillaOption Exercise type: European Payoff: Vanilla', vanilla_str)
def test_mc_variance_swap(self):
""" test mc variance engine vs expected result
"""
vols = []
dates = []
interm_date = self.today + int(0.1 * 365 + 0.5)
exercise = EuropeanExercise(self.ex_date)
dates.append(interm_date)
dates.append(self.ex_date)
vols.append(0.1)
vols.append(self.values['v'])
# Exercising code using BlackVarianceCurve because BlackVarianceSurface
# is unreliable. Result should be v*v for arbitrary t1 and v1
# (as long as 0<=t1<t and 0<=v1<v)
vol_ts = BlackVarianceCurve(self.today, dates, vols, self.dc, True)
stoch_process = BlackScholesMertonProcess(self.spot, self.q_ts,
self.r_ts, vol_ts)
engine = MCVarianceSwapEngine(
stoch_process,
time_steps_per_year=250,
required_samples=1023,
seed=42,
)
variance_swap = VarianceSwap(
self.values['type'],
self.values['strike'],
self.values['nominal'],
self.today,
self.ex_date,
)
variance_swap.set_pricing_engine(engine)
calculated = variance_swap.variance
expected = 0.04
tol = 3.0e-4
error = abs(calculated - expected)
self.assertTrue(error < tol)
def test_analytic_cont_geom_av_price(self):
"""
"Testing analytic continuous geometric average-price Asians...")
data from "Option Pricing Formulas", Haug, pag.96-97
"""
exercise = EuropeanExercise(self.settlement_date)
option = ContinuousAveragingAsianOption(Geometric, self.payoff,
exercise)
engine = AnalyticContinuousGeometricAveragePriceAsianEngine(
self.black_scholes_merton_process)
option.set_pricing_engine(engine)
tolerance = 1.0e-4
self.assertAlmostEqual(4.6922,
option.net_present_value,
delta=tolerance)
# trying to approximate the continuous version with the discrete version
running_accumulator = 1.0
past_fixings = 0
fixing_dates = [self.today + i for i in range(91)]
engine2 = AnalyticDiscreteGeometricAveragePriceAsianEngine(
self.black_scholes_merton_process)
option2 = DiscreteAveragingAsianOption(
Geometric,
self.payoff,
exercise,
fixing_dates,
past_fixings=past_fixings,
running_accum=running_accumulator,
)
option2.set_pricing_engine(engine2)
tolerance = 3.0e-3
self.assertAlmostEqual(4.6922,
option.net_present_value,
delta=tolerance)
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 _get_option_npv(self):
""" Suboptimal getter for the npv.
FIXME: We currently have to recreate most of the objects because we do not
expose enough of the QuantLib api.
"""
# convert datetime object to QlDate
maturity = QlDate.from_datetime(self.maturity)
underlyingH = SimpleQuote(self.underlying)
# bootstrap the yield/dividend/vol curves
flat_term_structure = FlatForward(
reference_date = settlement_date,
forward = self.risk_free_rate,
daycounter = self.daycounter
)
flat_dividend_ts = FlatForward(
reference_date = settlement_date,
forward = self.dividend_yield,
daycounter = self.daycounter
)
flat_vol_ts = BlackConstantVol(
settlement_date, calendar, self.volatility, self.daycounter
)
black_scholes_merton_process = BlackScholesMertonProcess(
underlyingH, flat_dividend_ts, flat_term_structure,flat_vol_ts
)
payoff = PlainVanillaPayoff(self.option_type, self.strike)
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)
return european_option.net_present_value
def blsprice(spot, strike, risk_free_rate, time, volatility, option_type='Call', dividend=0.0):
""" """
spot = SimpleQuote(spot)
daycounter = Actual360()
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), volatility, daycounter)
process = BlackScholesMertonProcess(spot, dividend_ts, risk_free_ts, volatility_ts)
exercise_date = today() + 90
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
return option.npv
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.from_reference_date(
BootstrapTrait.ZeroYield, Interpolator.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))
# bootstrap the yield/dividend/vol curves
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)
payoff = PlainVanillaPayoff(option_type, strike)
european_exercise = EuropeanExercise(maturity)
european_option = VanillaOption(payoff, european_exercise)
method = 'Black-Scholes'
analytic_european_engine = AnalyticEuropeanEngine(black_scholes_merton_process)
european_option.set_pricing_engine(analytic_european_engine)
print('today: %s settlement: %s maturity: %s' %
(todays_date, settlement_date, maturity))
print('NPV: %f\n' % european_option.net_present_value)
### EOF #######################################################################
def test_analytic_cont_geo_av_price_greeks(self):
tolerance = {}
tolerance["delta"] = 1.0e-5
tolerance["gamma"] = 1.0e-5
# tolerance["theta"] = 1.0e-5
tolerance["rho"] = 1.0e-5
tolerance["divRho"] = 1.0e-5
tolerance["vega"] = 1.0e-5
opt_types = [Call, Put]
underlyings = [100.0]
strikes = [90.0, 100.0, 110.0]
q_rates = [0.04, 0.05, 0.06]
r_rates = [0.01, 0.05, 0.15]
lengths = [1, 2]
vols = [0.11, 0.50, 1.20]
spot = SimpleQuote(0.0)
q_rate = SimpleQuote(0.0)
r_rate = SimpleQuote(0.0)
vol = SimpleQuote(0.0)
q_ts = flat_rate(q_rate, self.daycounter)
r_ts = flat_rate(r_rate, self.daycounter)
vol_ts = BlackConstantVol(self.today, self.calendar, vol, self.daycounter)
process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
calculated = {}
expected = {}
for opt_type, strike, length in product(opt_types, strikes, lengths):
maturity = EuropeanExercise(self.today + length*Years)
payoff = PlainVanillaPayoff(opt_type, strike)
engine = AnalyticContinuousGeometricAveragePriceAsianEngine(process)
option = ContinuousAveragingAsianOption(Geometric, payoff, maturity)
option.set_pricing_engine(engine)
for u, m, n, v in product(underlyings, q_rates, r_rates, vols):
q = m
r = n
spot.value = u
q_rate.value = q
r_rate.value = r
vol.value = v
value = option.npv
calculated["delta"] = option.delta
calculated["gamma"] = option.gamma
# calculated["theta"] = option.theta
calculated["rho"] = option.rho
calculated["divRho"] = option.dividend_rho
calculated["vega"] = option.vega
if (value > spot.value*1.0e-5):
# perturb spot and get delta and gamma
du = u*1.0e-4
spot.value = u + du
value_p = option.npv
delta_p = option.delta
spot.value = u - du
value_m = option.npv
delta_m = option.delta
spot.value = u
expected["delta"] = (value_p - value_m)/(2*du)
expected["gamma"] = (delta_p - delta_m)/(2*du)
# perturb rates and get rho and dividend rho
dr = r*1.0e-4
r_rate.value = r + dr
value_p = option.npv
r_rate.value = r - dr
value_m = option.npv
r_rate.value = r
expected["rho"] = (value_p - value_m)/(2*dr)
dq = q*1.0e-4
q_rate.value = q + dq
value_p = option.npv
q_rate.value = q - dq
value_m = option.npv
q_rate.value = q
expected["divRho"] = (value_p - value_m)/(2*dq)
# perturb volatility and get vega
dv = v*1.0e-4
vol.value = v + dv
value_p = option.npv
vol.value = v - dv
value_m = option.npv
vol.value = v
expected["vega"] = (value_p - value_m)/(2*dv)
# perturb date and get theta
dt = self.daycounter.year_fraction(self.today - 1, self.today + 1)
self.settings.evaluation_date = self.today - 1
value_m = option.npv
self.settings.evaluation_date = self.today + 1
value_p = option.npv
self.settings.evaluation_date = self.today
expected["theta"] = (value_p - value_m)/dt
# compare
for greek, calcl in calculated.items():
expct = expected[greek]
tol = tolerance[greek]
error = relative_error(expct, calcl, u)
self.assertTrue(error < tol)
def test_bates_det_jump(self):
# this looks like a bug in QL:
# Bates Det Jump model does not have sigma as parameter, yet
# changing sigma changes the result!
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 1290)
exercise = EuropeanExercise(exercise_date)
option = VanillaOption(payoff, exercise)
risk_free_ts = flat_rate(0.02, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
spot = 1290
ival = {'delta': 3.6828677022272715e-06,
'kappa': 19.02581428347027,
'kappaLambda': 1.1209758060939223,
'lambda': 0.06524550732595163,
'nu': -1.8968106563601956,
'rho': -0.7480898462264719,
'sigma': 1.0206363887835108,
'theta': 0.01965384459461113,
'thetaLambda': 0.028915397380738218,
'v0': 0.06566800935242285}
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_1 = option.net_present_value
ival['sigma'] = 1.e-6
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_2 = option.net_present_value
if(abs(calc_1-calc_2) > 1.e-5):
print('calc 1 %f calc 2 %f' % (calc_1, calc_2))
self.assertNotEqual(calc_1, calc_2)
def test_bsm_hw(self):
print("Testing European option pricing for a BSM process" +
" with one-factor Hull-White model...")
dc = Actual365Fixed()
todays_date = today()
maturity_date = todays_date + Period(20, Years)
settings = Settings()
settings.evaluation_date = todays_date
spot = SimpleQuote(100)
q_ts = flat_rate(todays_date, 0.04, dc)
r_ts = flat_rate(todays_date, 0.0525, dc)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), 0.25, dc)
hullWhiteModel = HullWhite(r_ts, 0.00883, 0.00526)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
exercise = EuropeanExercise(maturity_date)
fwd = spot.value * q_ts.discount(maturity_date) / \
r_ts.discount(maturity_date)
payoff = PlainVanillaPayoff(Call, fwd)
option = VanillaOption(payoff, exercise)
tol = 1e-8
corr = [-0.75, -0.25, 0.0, 0.25, 0.75]
expectedVol = [
0.217064577, 0.243995801, 0.256402830, 0.268236596, 0.290461343
]
for c, v in zip(corr, expectedVol):
bsm_hw_engine = AnalyticBSMHullWhiteEngine(c, bsm_process,
hullWhiteModel)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(bsm_hw_engine)
npv = option.npv
compVolTS = BlackConstantVol(todays_date, NullCalendar(), v, dc)
bs_process = BlackScholesMertonProcess(spot, q_ts, r_ts, compVolTS)
bsEngine = AnalyticEuropeanEngine(bs_process)
comp = VanillaOption(payoff, exercise)
comp.set_pricing_engine(bsEngine)
impliedVol = comp.implied_volatility(npv,
bs_process,
1e-10,
500,
min_vol=0.1,
max_vol=0.4)
if (abs(impliedVol - v) > tol):
print("Failed to reproduce implied volatility cor: %f" % c)
print("calculated: %f" % impliedVol)
print("expected : %f" % v)
if abs((comp.npv - npv) / npv) > tol:
print("Failed to reproduce NPV")
print("calculated: %f" % comp.npv)
print("expected : %f" % npv)
self.assertAlmostEqual(impliedVol, v, delta=tol)
self.assertAlmostEqual(comp.npv / npv, 1, delta=tol)
def test_zanette(self):
"""
From paper by A. Zanette et al.
"""
dc = Actual365Fixed()
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
# constant yield and div curves
dates = [todays_date + Period(i, Years) for i in range(3)]
rates = [0.04 for i in range(3)]
divRates = [0.03 for i in range(3)]
r_ts = ZeroCurve(dates, rates, dc)
q_ts = ZeroCurve(dates, divRates, dc)
s0 = SimpleQuote(100)
# Heston model
v0 = .1
kappa_v = 2
theta_v = 0.1
sigma_v = 0.3
rho_sv = -0.5
hestonProcess = HestonProcess(risk_free_rate_ts=r_ts,
dividend_ts=q_ts,
s0=s0,
v0=v0,
kappa=kappa_v,
theta=theta_v,
sigma=sigma_v,
rho=rho_sv)
hestonModel = HestonModel(hestonProcess)
# Hull-White
kappa_r = 1
sigma_r = .2
hullWhiteProcess = HullWhiteProcess(r_ts, a=kappa_r, sigma=sigma_r)
strike = 100
maturity = 1
type = Call
maturity_date = todays_date + Period(maturity, Years)
exercise = EuropeanExercise(maturity_date)
payoff = PlainVanillaPayoff(type, strike)
option = VanillaOption(payoff, exercise)
def price_cal(rho, tGrid):
fd_hestonHwEngine = FdHestonHullWhiteVanillaEngine(
hestonModel, hullWhiteProcess, rho, tGrid, 100, 40, 20, 0,
True, FdmSchemeDesc.Hundsdorfer())
option.set_pricing_engine(fd_hestonHwEngine)
return option.npv
calc_price = []
for rho in [-0.5, 0, .5]:
for tGrid in [50, 100, 150, 200]:
tmp = price_cal(rho, tGrid)
print("rho (S,r): %f Ns: %d Price: %f" % (rho, tGrid, tmp))
calc_price.append(tmp)
expected_price = [
11.38,
] * 4 + [
12.79,
] * 4 + [
14.06,
] * 4
np.testing.assert_almost_equal(calc_price, expected_price, 2)
def test_compare_BsmHW_HestonHW(self):
"""
From Quantlib test suite
"""
print("Comparing European option pricing for a BSM " +
"process with one-factor Hull-White model...")
dc = Actual365Fixed()
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
tol = 1.e-2
spot = SimpleQuote(100)
dates = [todays_date + Period(i, Years) for i in range(40)]
rates = [0.01 + 0.0002 * np.exp(np.sin(i / 4.0)) for i in range(40)]
divRates = [0.02 + 0.0001 * np.exp(np.sin(i / 5.0)) for i in range(40)]
s0 = SimpleQuote(100)
r_ts = ZeroCurve(dates, rates, dc)
q_ts = ZeroCurve(dates, divRates, dc)
vol = SimpleQuote(0.25)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), vol.value, dc)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
variance = vol.value * vol.value
hestonProcess = HestonProcess(risk_free_rate_ts=r_ts,
dividend_ts=q_ts,
s0=s0,
v0=variance,
kappa=5.0,
theta=variance,
sigma=1e-4,
rho=0.0)
hestonModel = HestonModel(hestonProcess)
hullWhiteModel = HullWhite(r_ts, a=0.01, sigma=0.01)
bsmhwEngine = AnalyticBSMHullWhiteEngine(0.0, bsm_process,
hullWhiteModel)
hestonHwEngine = AnalyticHestonHullWhiteEngine(hestonModel,
hullWhiteModel, 128)
tol = 1e-5
strikes = [0.25, 0.5, 0.75, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5, 2.0, 4.0]
maturities = [1, 2, 3, 5, 10, 15, 20, 25, 30]
types = [Put, Call]
for type in types:
for strike in strikes:
for maturity in maturities:
maturity_date = todays_date + Period(maturity, Years)
exercise = EuropeanExercise(maturity_date)
fwd = strike * s0.value * \
q_ts.discount(maturity_date) / \
r_ts.discount(maturity_date)
payoff = PlainVanillaPayoff(type, fwd)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(bsmhwEngine)
calculated = option.npv
option.set_pricing_engine(hestonHwEngine)
expected = option.npv
if ((np.abs(expected - calculated) > calculated * tol)
and (np.abs(expected - calculated) > tol)):
cp = PAYOFF_TO_STR[type]
print("Failed to reproduce npv")
print("strike : %f" % strike)
print("maturity : %d" % maturity)
print("type : %s" % cp)
self.assertAlmostEqual(expected, calculated, delta=tol)
def test_compare_bsm_bsmhw_hestonhw(self):
dc = Actual365Fixed()
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
tol = 1.e-2
spot = SimpleQuote(100)
dates = [todays_date + Period(i, Years) for i in range(40)]
rates = [0.01 + 0.0002 * np.exp(np.sin(i / 4.0)) for i in range(40)]
divRates = [0.02 + 0.0001 * np.exp(np.sin(i / 5.0)) for i in range(40)]
s0 = SimpleQuote(100)
r_ts = ZeroCurve(dates, rates, dc)
q_ts = ZeroCurve(dates, divRates, dc)
vol = SimpleQuote(0.25)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), vol.value, dc)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
payoff = PlainVanillaPayoff(Call, 100)
exercise = EuropeanExercise(dates[1])
option = VanillaOption(payoff, exercise)
analytic_european_engine = AnalyticEuropeanEngine(bsm_process)
option.set_pricing_engine(analytic_european_engine)
npv_bsm = option.npv
variance = vol.value * vol.value
hestonProcess = HestonProcess(risk_free_rate_ts=r_ts,
dividend_ts=q_ts,
s0=s0,
v0=variance,
kappa=5.0,
theta=variance,
sigma=1e-4,
rho=0.0)
hestonModel = HestonModel(hestonProcess)
hullWhiteModel = HullWhite(r_ts, a=0.01, sigma=0.01)
bsmhwEngine = AnalyticBSMHullWhiteEngine(0.0, bsm_process,
hullWhiteModel)
hestonHwEngine = AnalyticHestonHullWhiteEngine(hestonModel,
hullWhiteModel, 128)
hestonEngine = AnalyticHestonEngine(hestonModel, 144)
option.set_pricing_engine(hestonEngine)
npv_heston = option.npv
option.set_pricing_engine(bsmhwEngine)
npv_bsmhw = option.npv
option.set_pricing_engine(hestonHwEngine)
npv_hestonhw = option.npv
print("calculated with BSM: %f" % npv_bsm)
print("BSM-HW: %f" % npv_bsmhw)
print("Heston: %f" % npv_heston)
print("Heston-HW: %f" % npv_hestonhw)
self.assertAlmostEqual(npv_bsm, npv_bsmhw, delta=tol)
self.assertAlmostEqual(npv_bsm, npv_hestonhw, delta=tol)
hestonModel = HestonModel(hestonProcess)
# Hull-White
kappa_r = 1
sigma_r = .2
hullWhiteProcess = HullWhiteProcess(r_ts, a=kappa_r, sigma=sigma_r)
strike = 100
maturity = 1
type = Call
maturity_date = todays_date + Period(maturity, Years)
exercise = EuropeanExercise(maturity_date)
payoff = PlainVanillaPayoff(type, strike)
option = VanillaOption(payoff, exercise)
def price_cal(rho, tGrid):
fd_hestonHwEngine = FdHestonHullWhiteVanillaEngine(
hestonModel, hullWhiteProcess, rho, tGrid, 100, 40, 20, 0, True,
FdmSchemeDesc.Hundsdorfer())
option.set_pricing_engine(fd_hestonHwEngine)
return option.npv
calc_price = []
