def test_american_vanilla_option_with_earliest_date_wrong_order(self):
with self.assertRaises(RuntimeError):
AmericanExercise(
self.settlement_date,
self.maturity
)
def test_american_vanilla_option(self):
american_exercise = AmericanExercise(self.maturity)
american_option = VanillaOption(self.payoff, american_exercise)
engine = BaroneAdesiWhaleyApproximationEngine(
self.black_scholes_merton_process)
american_option.set_pricing_engine(engine)
self.assertAlmostEquals(4.459628, american_option.net_present_value, 6)
def test_dividend_american_option(self):
american_exercise = AmericanExercise(self.maturity)
american_option = DividendVanillaOption(self.payoff, american_exercise,
self.dividend_dates,
self.dividends)
engine = FDDividendAmericanEngine('CrankNicolson',
self.black_scholes_merton_process,
self.american_time_steps,
self.american_grid_points)
american_option.set_pricing_engine(engine)
#Note slightly different value using CrankNicolson
self.assertAlmostEquals(4.485992, american_option.net_present_value, 6)
def test_dividend_american_option_implied_volatility(self):
american_exercise = AmericanExercise(self.maturity)
american_option = DividendVanillaOption(self.payoff, american_exercise,
self.dividend_dates,
self.dividends)
engine = FdBlackScholesVanillaEngine(self.black_scholes_merton_process,
self.american_time_steps,
self.american_grid_points)
american_option.set_pricing_engine(engine)
implied_volatility = american_option.implied_volatility(
self.target_price, self.black_scholes_merton_process,
self.accuracy, self.max_evaluations, self.min_vol, self.max_vol)
self.assertAlmostEqual(0.200, implied_volatility, 3)
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))
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())