def make_rate_helper(market, quote, reference_date=None):
"""
Wrapper for deposit and swaps rate helpers makers
TODO: class method of RateHelper?
"""
rate_type, tenor, quote_value = quote
if rate_type == 'SWAP':
libor_index = market._floating_rate_index
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
helper = SwapRateHelper.from_tenor(
quote_value, Period(tenor),
market._floating_rate_index.fixing_calendar,
Period(market._params.fixed_leg_period).frequency,
BusinessDayConvention.from_name(
market._params.fixed_leg_convention),
DayCounter.from_name(market._params.fixed_leg_daycount),
libor_index, spread, fwdStart)
elif rate_type == 'DEP':
end_of_month = True
helper = DepositRateHelper(
quote_value, Period(tenor), market._params.settlement_days,
market._floating_rate_index.fixing_calendar,
market._floating_rate_index.business_day_convention, end_of_month,
DayCounter.from_name(market._deposit_daycount))
elif rate_type == 'ED':
if reference_date is None:
raise Exception("Reference date needed with ED Futures data")
forward_date = next_imm_date(reference_date, tenor)
helper = FuturesRateHelper(
price=SimpleQuote(quote_value),
imm_date=qldate_from_pydate(forward_date),
length_in_months=3,
calendar=market._floating_rate_index.fixing_calendar,
convention=market._floating_rate_index.business_day_convention,
end_of_month=True,
day_counter=DayCounter.from_name(
market._params.floating_leg_daycount))
elif rate_type.startswith('ER'):
# TODO For Euribor futures, we found it useful to supply the `imm_date`
# parameter directly, instead of as a number of periods from the
# evaluation date, as for ED futures. To achieve this, we pass the
# `imm_date` in the `tenor` field of the quote.
helper = FuturesRateHelper(
price=SimpleQuote(quote_value),
imm_date=tenor,
length_in_months=3,
calendar=market._floating_rate_index.fixing_calendar,
convention=market._floating_rate_index.business_day_convention,
end_of_month=True,
day_counter=DayCounter.from_name(
market._params.floating_leg_daycount))
else:
raise Exception("Rate type %s not supported" % rate_type)
return helper
def example03():
print("example 3:\n")
todays_date = Date(13, 6, 2011)
Settings.instance().evaluation_date = todays_date
quotes = [0.00445, 0.00949, 0.01234, 0.01776, 0.01935, 0.02084]
tenors = [1, 2, 3, 6, 9, 12]
calendar = WeekendsOnly()
deps = [
DepositRateHelper(q, Period(t, Months), 2, calendar, ModifiedFollowing,
False, Actual360()) for q, t in zip(quotes, tenors)
]
quotes = [
0.01652, 0.02018, 0.02303, 0.02525, 0.0285, 0.02931, 0.03017, 0.03092,
0.03160, 0.03231, 0.03367, 0.03419, 0.03411, 0.03411, 0.03412
]
tenors = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 25, 30]
swaps = [
SwapRateHelper.from_tenor(q, Period(t, Years), calendar, Annual,
ModifiedFollowing, Thirty360(), Euribor6M(),
SimpleQuote(0))
for q, t in zip(quotes, tenors)
]
yield_helpers = deps + swaps
isda_yts = PiecewiseYieldCurve(BootstrapTrait.Discount,
Interpolator.LogLinear, 0, WeekendsOnly(),
yield_helpers, Actual365Fixed())
spreads = [0.007927, 0.012239, 0.016979, 0.019271, 0.020860]
tenors = [1, 3, 5, 7, 10]
spread_helpers = [SpreadCdsHelper(0.007927, Period(6, Months), 1,
WeekendsOnly(), Quarterly, Following, Rule.CDS2015,
Actual360(), 0.4, isda_yts, True, True,
Date(), Actual360(True), True, PricingModel.ISDA)] + \
[SpreadCdsHelper(s, Period(t, Years), 1, WeekendsOnly(), Quarterly, Following, Rule.CDS2015,
Actual360(), 0.4, isda_yts, True, True, Date(), Actual360(True), True,
PricingModel.ISDA)
for s, t in zip(spreads, tenors)]
isda_cts = PiecewiseDefaultCurve(ProbabilityTrait.SurvivalProbability,
Interpolator.LogLinear, 0, WeekendsOnly(),
spread_helpers, Actual365Fixed())
isda_pricer = IsdaCdsEngine(isda_cts, 0.4, isda_yts)
print("Isda yield curve:")
for h in yield_helpers:
d = h.latest_date
t = isda_yts.time_from_reference(d)
print(d, t, isda_yts.zero_rate(d, Actual365Fixed()).rate)
print()
print("Isda credit curve:")
for h in spread_helpers:
d = h.latest_date
t = isda_cts.time_from_reference(d)
print(d, t, isda_cts.survival_probability(d))
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))
def example03():
print("example 3:\n")
todays_date = Date(13, 6, 2011)
Settings.instance().evaluation_date = todays_date
quotes = [0.00445, 0.00949, 0.01234, 0.01776, 0.01935, 0.02084]
tenors = [1, 2, 3, 6, 9, 12]
calendar = WeekendsOnly()
deps = [DepositRateHelper(q, Period(t, Months), 2, calendar, ModifiedFollowing, False, Actual360())
for q, t in zip(quotes, tenors)]
quotes = [0.01652, 0.02018, 0.02303, 0.02525, 0.0285, 0.02931, 0.03017, 0.03092, 0.03160, 0.03231,
0.03367, 0.03419, 0.03411, 0.03411, 0.03412]
tenors = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 25, 30]
swaps = [SwapRateHelper.from_tenor(q, Period(t, Years),
calendar, Annual, ModifiedFollowing,
Thirty360(), Euribor6M(), SimpleQuote(0)) for q, t
in zip(quotes, tenors)]
yield_helpers = deps + swaps
isda_yts = PiecewiseYieldCurve(BootstrapTrait.Discount, Interpolator.LogLinear, 0,
WeekendsOnly(), yield_helpers, Actual365Fixed())
spreads = [0.007927, 0.012239, 0.016979, 0.019271, 0.020860]
tenors = [1, 3, 5, 7, 10]
spread_helpers = [SpreadCdsHelper(0.007927, Period(6, Months), 1,
WeekendsOnly(), Quarterly, Following, Rule.CDS2015,
Actual360(), 0.4, isda_yts, True, True,
Date(), Actual360(True), True, PricingModel.ISDA)] + \
[SpreadCdsHelper(s, Period(t, Years), 1, WeekendsOnly(), Quarterly, Following, Rule.CDS2015,
Actual360(), 0.4, isda_yts, True, True, Date(), Actual360(True), True,
PricingModel.ISDA)
for s, t in zip(spreads, tenors)]
isda_cts = PiecewiseDefaultCurve(ProbabilityTrait.SurvivalProbability,
Interpolator.LogLinear, 0, WeekendsOnly(), spread_helpers,
Actual365Fixed())
isda_pricer = IsdaCdsEngine(isda_cts, 0.4, isda_yts)
print("Isda yield curve:")
for h in yield_helpers:
d = h.latest_date
t = isda_yts.time_from_reference(d)
print(d, t, isda_yts.zero_rate(d, Actual365Fixed()).rate)
print()
print("Isda credit curve:")
for h in spread_helpers:
d = h.latest_date
t = isda_cts.time_from_reference(d)
print(d, t, isda_cts.survival_probability(d))
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))
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 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 make_rate_helper(market, quote, reference_date=None):
"""
Wrapper for deposit and swaps rate helpers makers
TODO: class method of RateHelper?
"""
rate_type, tenor, quote_value = quote
if rate_type == 'SWAP':
libor_index = market._floating_rate_index
spread = SimpleQuote(0)
fwdStart = Period(0, Days)
helper = SwapRateHelper.from_tenor(
quote_value,
Period(tenor),
market._floating_rate_index.fixing_calendar,
code_to_frequency(market._params.fixed_leg_period),
BusinessDayConvention.from_name(
market._params.fixed_leg_convention),
DayCounter.from_name(market._params.fixed_leg_daycount),
libor_index, spread, fwdStart)
elif rate_type == 'DEP':
end_of_month = True
helper = DepositRateHelper(
quote_value,
Period(tenor),
market._params.settlement_days,
market._floating_rate_index.fixing_calendar,
market._floating_rate_index.business_day_convention,
end_of_month,
DayCounter.from_name(market._deposit_daycount))
elif rate_type == 'ED':
if reference_date is None:
raise Exception("Reference date needed with ED Futures data")
forward_date = next_imm_date(reference_date, tenor)
helper = FuturesRateHelper(
rate =SimpleQuote(quote_value),
imm_date = qldate_from_pydate(forward_date),
length_in_months = 3,
calendar = market._floating_rate_index.fixing_calendar,
convention = market._floating_rate_index.business_day_convention,
end_of_month = True,
day_counter = DayCounter.from_name(
market._params.floating_leg_daycount))
elif rate_type.startswith('ER'):
# TODO For Euribor futures, we found it useful to supply the `imm_date`
# parameter directly, instead of as a number of periods from the
# evaluation date, as for ED futures. To achieve this, we pass the
# `imm_date` in the `tenor` field of the quote.
helper = FuturesRateHelper(
rate=SimpleQuote(quote_value),
imm_date=tenor,
length_in_months=3,
calendar=market._floating_rate_index.fixing_calendar,
convention=market._floating_rate_index.business_day_convention,
end_of_month=True,
day_counter=DayCounter.from_name(
market._params.floating_leg_daycount))
else:
raise Exception("Rate type %s not supported" % rate_type)
return helper
futuresHelpers = [ FuturesRateHelper(futures[d],
d, months,
calendar, ModifiedFollowing,
True, day_counter)
for d in futures.keys() ]
settlementDays = 2
fixedLegFrequency = Annual
fixedLegTenor = Period(1,Years)
fixedLegAdjustment = Unadjusted
fixedLegDayCounter = Thirty360()
floatingLegFrequency = Semiannual
floatingLegTenor = Period(6,Months)
floatingLegAdjustment = ModifiedFollowing
swapHelpers = [ SwapRateHelper.from_tenor(swaps[(n,unit)],
Period(n,unit), calendar,
fixedLegFrequency, fixedLegAdjustment,
fixedLegDayCounter, Euribor6M())
for n, unit in swaps.keys() ]
### Curve building
ts_daycounter = ActualActual(ISDA)
# term-structure construction
helpers = depositHelpers + swapHelpers
depoSwapCurve = PiecewiseYieldCurve.from_reference_date(
BootstrapTrait.Discount, Interpolator.LogLinear, settlementDate, helpers, ts_daycounter
)
helpers = depositHelpers[:2] + futuresHelpers + swapHelpers[1:]
depoFuturesSwapCurve = PiecewiseYieldCurve.from_reference_date(
