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%matplotlib inline
import numpy as np
import pandas as pd
pd.set_option('precision', 2)
from QuantLib import *

Parameter



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maturity_date = Date(30, 6, 2018)
start_date = Date(1, 1, 2018)

spot = 1.
strike = 1.
barrier = 1.5

volatility = 0.30
risk_free_rate = 0.
dividend_rate = 0.
day_count = Actual365Fixed()
calendar = China(China.SSE)

Market Data



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calculation_date = start_date
Settings.instance().evaluationDate = calculation_date

spot_handle = RelinkableQuoteHandle(SimpleQuote(spot))
vol_handle =  RelinkableQuoteHandle(SimpleQuote(volatility))

flat_ts = YieldTermStructureHandle(FlatForward(calculation_date, risk_free_rate, day_count))
dividend_yield = YieldTermStructureHandle(FlatForward(calculation_date, dividend_rate, day_count))
flat_vol_ts = BlackVolTermStructureHandle(BlackConstantVol(calculation_date, calendar, vol_handle, day_count))

bsm_process = BlackScholesMertonProcess(spot_handle, dividend_yield, flat_ts, flat_vol_ts)



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payoff = PlainVanillaPayoff(Option.Call, strike)
exercise = EuropeanExercise(maturity_date)

option = BarrierOption(Barrier.UpOut, barrier=barrier, rebate=0., payoff=payoff, exercise=exercise)

Analytic Method



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%%time
engine = AnalyticBarrierEngine(bsm_process)
option.setPricingEngine(engine)

bsm_price = option.NPV()
print("BSM european theoreticl price is {0:.4f}".format(bsm_price))

FDM method



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%%time
engine = FdBlackScholesBarrierEngine(bsm_process, 200, 200)
option.setPricingEngine(engine)

bsm_price = option.NPV()
bsm_delta = option.delta()
print("FDM european price is {0:.4f}".format(bsm_price))
print("FDM european delta is {0:.4f}".format(bsm_delta))

MC Method



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engine = MCBarrierEngine(bsm_process, 'ld', 100, brownianBridge=True, antitheticVariate=True, requiredSamples=5000)
option.setPricingEngine(engine)

bsm_price = option.NPV()
print("MC european price is {0:.4f}".format(bsm_price))

European Call Approximation



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multiplyer = 1000.
p_gap = barrier - strike
x_gap = p_gap / (multiplyer - 1.)



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payoff1 = PlainVanillaPayoff(Option.Call, strike)
payoff2 = PlainVanillaPayoff(Option.Call, barrier)
payoff3 = PlainVanillaPayoff(Option.Call, barrier + x_gap)

exercise = EuropeanExercise(maturity_date)
option1 = VanillaOption(payoff1, exercise)
option2 = VanillaOption(payoff2, exercise)
option3 = VanillaOption(payoff3, exercise)



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%%time
engine = AnalyticEuropeanEngine(bsm_process)
option1.setPricingEngine(engine)
option2.setPricingEngine(engine)
option3.setPricingEngine(engine)

bsm_price = option1.NPV() - multiplyer * option2.NPV() + (multiplyer - 1.) * option3.NPV()
print("BSM european theoreticl price is {0:.4f}".format(bsm_price))



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