def __init__(self, btype):
# global data
self.todaysDate = ql.Date(15, ql.May, 1998)
ql.Settings.instance().evaluationDate = self.todaysDate
self.settlementDate = ql.Date(17, ql.May, 1998)
self.riskFreeQuote = ql.SimpleQuote(0.05)
self.riskFreeRate = ql.FlatForward(self.settlementDate,
ql.QuoteHandle(self.riskFreeQuote),
ql.Actual365Fixed())
# option parameters
self.exercise = ql.EuropeanExercise(ql.Date(17, ql.May, 1999))
self.payoff = ql.PlainVanillaPayoff(ql.Option.Call, 8.0)
# market data
self.underlying1 = ql.SimpleQuote(10.0)
self.volatility1 = ql.BlackConstantVol(self.todaysDate, 0.20,
ql.Actual365Fixed())
self.dividendYield1 = ql.FlatForward(self.settlementDate, 0.05,
ql.Actual365Fixed())
self.underlying2 = ql.SimpleQuote(7.0)
self.volatility2 = ql.BlackConstantVol(self.todaysDate, 0.10,
ql.Actual365Fixed())
self.dividendYield2 = ql.FlatForward(self.settlementDate, 0.05,
ql.Actual365Fixed())
self.process1 = ql.BlackScholesMertonProcess(
ql.QuoteHandle(self.underlying1),
ql.YieldTermStructureHandle(self.dividendYield1),
ql.YieldTermStructureHandle(self.riskFreeRate),
ql.BlackVolTermStructureHandle(self.volatility1),
)
self.process2 = ql.BlackScholesMertonProcess(
ql.QuoteHandle(self.underlying2),
ql.YieldTermStructureHandle(self.dividendYield2),
ql.YieldTermStructureHandle(self.riskFreeRate),
ql.BlackVolTermStructureHandle(self.volatility2),
)
self.procs = ql.StochasticProcessVector()
self.procs.push_back(self.process1)
self.procs.push_back(self.process2)
self.matrix = ql.Matrix(2, 2)
self.matrix[0][0] = 1.0
self.matrix[1][1] = 1.0
self.matrix[0][1] = 0.25
self.matrix[1][0] = 0.25
self.process = ql.StochasticProcessArray(self.procs, self.matrix)
self.engine = ql.MCBasketEngine("lowdiscrepancy",
timeStepsPerYear=1,
requiredTolerance=0.02,
seed=42)
if btype == "min":
bpayoff = ql.MinBasketPayoff(self.payoff)
elif btype == "max":
bpayoff = ql.MaxBasketPayoff(self.payoff)
else:
bpayoff = ql.AverageBasketPayoff(self.payoff, 2)
self.option = ql.BasketOption(self.process, bpayoff, self.exercise,
self.engine)
process2 = ql.BlackScholesMertonProcess(
ql.QuoteHandle(underlying2),
ql.YieldTermStructureHandle(dividendYield2),
ql.YieldTermStructureHandle(riskFreeRate),
ql.BlackVolTermStructureHandle(volatility2),
)
matrix = ql.Matrix(2, 2)
matrix[0][0] = 1.0
matrix[1][1] = 1.0
matrix[0][1] = 0.5
matrix[1][0] = 0.5
process = ql.StochasticProcessArray([process1, process2], matrix)
basketoption = ql.BasketOption(ql.MaxBasketPayoff(payoff), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
print(basketoption.NPV())
basketoption = ql.BasketOption(ql.MinBasketPayoff(payoff), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
print(basketoption.NPV())
basketoption = ql.BasketOption(ql.AverageBasketPayoff(payoff, 2), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
def valueBasketCall(val_date,
settle_date,
maturity_days,
tmp_stock,
tmp_vol,
tmp_corr,
rf_rate=0.0,
strike=100.0,
dividend=0.0,
basketCallType='Min',
randMethod="pseudorandom",
_timeStepsPerYear=1,
_requiredTolerance=0.02,
_seed=42):
tic = time.time()
# Input Checks
no_stock = len(tmp_stock)
theo_no_corr = no_stock * (no_stock - 1) /2
if len(tmp_corr) != theo_no_corr:
print('Number of stocks (%d) and number of correlations (%d) do not match! Should be %d ' % (no_stock, len(tmp_corr), theo_no_corr))
return 0.0
if basketCallType not in ["Min","Max","Average"]:
print('Unsupported basket Call type %s, only ["Min","Max","Average"] are supported.' % basketCallType)
return 0.0
# Set dates
day_count = ql.Actual365Fixed()
py_val_date = datetime.strptime(val_date, '%Y-%m-%d')
ql_val_date = ql.Date(py_val_date.day, py_val_date.month, py_val_date.year)
py_settle_date = datetime.strptime(settle_date, '%Y-%m-%d')
ql_settle_date = ql.Date(py_settle_date.day, py_settle_date.month, py_settle_date.year)
py_maturity_date = py_val_date + timedelta(days=int(maturity_days))
ql_maturity_date = ql.Date(py_maturity_date.day, py_maturity_date.month, py_maturity_date.year)
# Set QL instance
ql.Settings.instance().evaluationDate = ql_val_date
# Create exercise object
exercise = ql.EuropeanExercise(ql_maturity_date)
# Create Payoff Object
payoff = ql.PlainVanillaPayoff(ql.Option.Call, strike)
# Create risk free rate object
riskFreeRate = ql.FlatForward(ql_settle_date, rf_rate, day_count)
# Create list of equity parameters
ql_underlying_list = [ql.SimpleQuote(i) for i in tmp_stock]
ql_vol_list = [ql.BlackConstantVol(ql_val_date, ql.TARGET(), i, day_count) for i in tmp_vol]
ql_div_list = [ql.FlatForward(ql_settle_date, dividend, day_count) for i in tmp_stock]
# Populate Correlation Matrix
matrix = populateCorrMatrix(tmp_corr, no_stock)
# Create list of QL processes for equity
ql_process_list =[ql.BlackScholesMertonProcess(
ql.QuoteHandle(ql_underlying_list[i]),
ql.YieldTermStructureHandle(ql_div_list[i]),
ql.YieldTermStructureHandle(riskFreeRate),
ql.BlackVolTermStructureHandle(ql_vol_list[i]),) for i in range(len(ql_underlying_list))]
if no_stock == 1:
# Use Black Scholes Formula to calculate European Call
#print("Single stock, use BS Formula!")
option = ql.VanillaOption(payoff, exercise)
bsm_process = ql_process_list[0]
option.setPricingEngine(ql.AnalyticEuropeanEngine(bsm_process))
else:
# Create QL Multi-variate Stochastic Process
process = ql.StochasticProcessArray(ql_process_list, matrix)
# Create Basket Option Object
if basketCallType == "Min":
option = ql.BasketOption(ql.MinBasketPayoff(payoff), exercise)
elif basketCallType == "Max":
option = ql.BasketOption(ql.MaxBasketPayoff(payoff), exercise)
elif basketCallType == "Average":
option = ql.BasketOption(ql.AverageBasketPayoff(payoff), exercise)
# Set Pricing Engine
option.setPricingEngine(ql.MCEuropeanBasketEngine(process,
randMethod,
timeStepsPerYear=_timeStepsPerYear,
requiredTolerance=_requiredTolerance,
seed=_seed)
)
p = option.NPV()
#p=0
toc = time.time()
#print(p, maturity_days, toc-tic)
return p
