def main():
# global data
todays_date = Date(15, May, 1998)
Settings.instance().evaluation_date = todays_date
settlement_date = Date(17, May, 1998)
risk_free_rate = FlatForward(
reference_date=settlement_date,
forward=0.06,
daycounter=Actual365Fixed()
)
# option parameters
exercise = AmericanExercise(
earliest_exercise_date = settlement_date,
latest_exercise_date = Date(17, May, 1999)
)
payoff = PlainVanillaPayoff(Put, 40.0)
# market data
underlying = SimpleQuote(36.0)
volatility = BlackConstantVol(todays_date, TARGET(), 0.20,
Actual365Fixed())
dividend_yield = FlatForward(
reference_date = settlement_date,
forward = 0.00,
daycounter = Actual365Fixed()
)
# report
header = '%19s' % 'method' + ' |' + \
' |'.join(['%17s' % tag for tag in ['value',
'estimated error',
'actual error' ] ])
print()
print(header)
print('-'*len(header))
refValue = None
def report(method, x, dx=None):
e = '%.4f' % abs(x - refValue)
x = '%.5f' % x
if dx:
dx = '%.4f' % dx
else:
dx = 'n/a'
print('%19s' % method + ' |' + \
' |'.join(['%17s' % y for y in [x, dx, e] ]))
# good to go
process = BlackScholesMertonProcess(
underlying, dividend_yield, risk_free_rate, volatility
)
option = VanillaOption(payoff, exercise)
refValue = 4.48667344
report('reference value', refValue)
# method: analytic
option.set_pricing_engine(BaroneAdesiWhaleyApproximationEngine(process))
report('Barone-Adesi-Whaley', option.net_present_value)
# method: finite differences
time_steps = 801
grid_points = 800
option.set_pricing_engine(FDAmericanEngine('CrankNicolson',
process, time_steps, grid_points))
report('finite differences', option.net_present_value)
print('This is work in progress.')
print('Some pricing engines are not yet interfaced.')
return
option.set_pricing_engine(BjerksundStenslandEngine(process))
report('Bjerksund-Stensland',option.NPV())
# method: binomial
timeSteps = 801
option.setPricingEngine(BinomialVanillaEngine(process,'jr',timeSteps))
report('binomial (JR)',option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process,'crr',timeSteps))
report('binomial (CRR)',option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process,'eqp',timeSteps))
report('binomial (EQP)',option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process,'trigeorgis',timeSteps))
report('bin. (Trigeorgis)',option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process,'tian',timeSteps))
report('binomial (Tian)',option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process,'lr',timeSteps))
report('binomial (LR)',option.NPV())
# 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 main():
# global data
todays_date = Date(15, May, 1998)
Settings.instance().evaluation_date = todays_date
settlement_date = Date(17, May, 1998)
risk_free_rate = FlatForward(reference_date=settlement_date,
forward=0.06,
daycounter=Actual365Fixed())
# option parameters
exercise = AmericanExercise(earliest_exercise_date=settlement_date,
latest_exercise_date=Date(17, May, 1999))
payoff = PlainVanillaPayoff(Put, 40.0)
# market data
underlying = SimpleQuote(36.0)
volatility = BlackConstantVol(todays_date, TARGET(), 0.20,
Actual365Fixed())
dividend_yield = FlatForward(reference_date=settlement_date,
forward=0.00,
daycounter=Actual365Fixed())
# report
header = '%19s' % 'method' + ' |' + \
' |'.join(['%17s' % tag for tag in ['value',
'estimated error',
'actual error']])
print()
print(header)
print('-' * len(header))
refValue = None
def report(method, x, dx=None):
e = '%.4f' % abs(x - refValue)
x = '%.5f' % x
if dx:
dx = '%.4f' % dx
else:
dx = 'n/a'
print('%19s' % method + ' |' +
' |'.join(['%17s' % y for y in [x, dx, e]]))
# good to go
process = BlackScholesMertonProcess(underlying, dividend_yield,
risk_free_rate, volatility)
option = VanillaOption(payoff, exercise)
refValue = 4.48667344
report('reference value', refValue)
# method: analytic
option.set_pricing_engine(BaroneAdesiWhaleyApproximationEngine(process))
report('Barone-Adesi-Whaley', option.net_present_value)
# method: finite differences
time_steps = 801
grid_points = 800
option.set_pricing_engine(
FDAmericanEngine('CrankNicolson', process, time_steps, grid_points))
report('finite differences', option.net_present_value)
print('This is work in progress.')
print('Some pricing engines are not yet interfaced.')
return
option.set_pricing_engine(BjerksundStenslandEngine(process))
report('Bjerksund-Stensland', option.NPV())
# method: binomial
timeSteps = 801
option.setPricingEngine(BinomialVanillaEngine(process, 'jr', timeSteps))
report('binomial (JR)', option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process, 'crr', timeSteps))
report('binomial (CRR)', option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process, 'eqp', timeSteps))
report('binomial (EQP)', option.NPV())
option.setPricingEngine(
BinomialVanillaEngine(process, 'trigeorgis', timeSteps))
report('bin. (Trigeorgis)', option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process, 'tian', timeSteps))
report('binomial (Tian)', option.NPV())
option.setPricingEngine(BinomialVanillaEngine(process, 'lr', timeSteps))
report('binomial (LR)', option.NPV())
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)