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 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 = BlackVolTermStructure(
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 [1,2,3,4,5,6,7,12]]
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):
# Rate description ___ record of the rate
swapHandle = SimpleQuote(rate)
# 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(swapHandle,swapIndex))
# ++++++++++++++++++ Now the creation of the yield curve
riskFreeTS = term_structure_factory('zero', 'linear', settlementDate, instruments, dayCounter)
# ++++++++++++++++++ build of the underlying process : with a Black-Scholes model
bsProcess = BlackScholesProcess(underlying_priceH, riskFreeTS, flatVolTS)
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++ Description of the option +++++++++++++++++++++++++++++++++++++++
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Option_name = "IBM Option"
maturity = Date(26, Jan,2013)
strike = 190
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)
print "**********************************"
print "Description of the option: ", Option_name
print "Date of maturity: ", maturity
print "Type of the 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 = 0.0 #//0.75
nextDividendDate = Date(10,Feb,2012)
# HERE we have make the assumption that the dividend will grow with the quarterly croissance:
dividendCroissance = 1.03
dividendfrequence = 3 * Months
dividendDates = []
dividends = []
d = nextDividentDate
while d < maturity:
dividendDates.append(d)
dividend.append(dividend)
d += dividendfrequence
dividend *= dividendCroissance
print "Discrete dividends "
print "Dates Dividends "
for date, div in zip(dividendDates, dividend):
print date, " ", div
# ++++++++++++++++++ Description of the final payoff
payoff = PlainVanillaPayoff(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.setPricingEngine(dividendEuropeanEngine)
dividendAmericanOption.setPricingEngine(dividendAmericanEngine)
# just to test
europeanOption.setPricingEngine(europeanEngine)
americanOption.setPricingEngine(americanEngine)
# Now we make all the needing calcul
# ... and final results
print "NPV of the European Option with discrete dividends=0: ", dividendEuropeanOption.NPV()
print "NPV of the European Option without dividend: ", europeanOption.NPV()
print "NPV of the American Option with discrete dividends=0: ", dividendAmericanOption.NPV()
print "NPV of the American Option without dividend: ", americanOption.NPV()
# just a single test
print "ZeroRate with a maturity at ", maturity, ": ", \
riskFreeTS.currentLink().zeroRate(maturity, dayCounter, Simple)
