[Quantlib-users] How to price the arithmetic option using python quantlib

[floatwing]

I tried many times, but it went wrong and i don't know how to fix it.
I used the DiscreteAveragingAsianOption method to price the arithmetic
option where i used the MCDiscreteArithmeticAPEngine to generize the Monte
Carlo path of Underlying prices. But I cann't correctly quote the two
functions. If there are any python docs or examples to price the arithmetc
option?
I searched the internet for a long time with little materials.Some of my
codes are as follows:

process2 = GeneralizedBlackScholesProcess(QuoteHandle(underlying),

YieldTermStructureHandle(dividendYield),

YieldTermStructureHandle(riskFreeRate),

BlackVolTermStructureHandle(volatility))

#asian settings
averageType = Average().Arithmetic
runningAccumulator = 1
pastFixings = 0
fixingDates = []
isBrownianbridge = False
isAntitheticvariate = True
isControlvariate = False
requiredSamples = 10000
requiredTolerance = 1e-3
maxSamples = 100000
seed = 42
enginestr = 'pr'
option = DiscreteAveragingAsianOption(averageType, runningAccumulator,
pastFixings, fixingDates, payoff, excercise)
engine = MCDiscreteArithmeticAPEngine(process2, enginestr, isBrownianbridge,
isAntitheticvariate, isControlvariate, requiredSamples, requiredTolerance,
maxSamples, seed)

Plz tell what's wrong or how to quote the two functions!!



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[Luigi Ballabio]

If you're asking for the next step, that would be

option.setPricingEngine(engine)
print option.NPV()

If you tried that and didn't work, it might be because you're not defining
any fixing dates, and a discrete-averaging Asian option needs some.

If it still doesn't work, please attach a complete example.

Luigi

Post by floatwing
I tried many times, but it went wrong and i don't know how to fix it.
I used the DiscreteAveragingAsianOption method to price the arithmetic
option where i used the MCDiscreteArithmeticAPEngine to generize the Monte
Carlo path of Underlying prices. But I cann't correctly quote the two
functions. If there are any python docs or examples to price the arithmetc
option?
I searched the internet for a long time with little materials.Some of my
process2 = GeneralizedBlackScholesProcess(QuoteHandle(underlying),
YieldTermStructureHandle(dividendYield),
YieldTermStructureHandle(riskFreeRate),
BlackVolTermStructureHandle(volatility))
#asian settings
averageType = Average().Arithmetic
runningAccumulator = 1
pastFixings = 0
fixingDates = []
isBrownianbridge = False
isAntitheticvariate = True
isControlvariate = False
requiredSamples = 10000
requiredTolerance = 1e-3
maxSamples = 100000
seed = 42
enginestr = 'pr'
option = DiscreteAveragingAsianOption(averageType, runningAccumulator,
pastFixings, fixingDates, payoff, excercise)
engine = MCDiscreteArithmeticAPEngine(process2, enginestr,
isBrownianbridge,
isAntitheticvariate, isControlvariate, requiredSamples, requiredTolerance,
maxSamples, seed)
Plz tell what's wrong or how to quote the two functions!!
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[floatwing]

Thank you for your reply first! I am not asking for the next step. I mean
there might be argument errors in the MCDiscreteGeometricAPEngine
function(the arguments the function needs is hard to find in python), event
when i set the fixingDates = [Date(30,12,2017)] for example.By the way, what
does 'fixingDates' mean? I will attatch the new code to the poster, can you
have a check what's wrong to my code?It result in the python kernel
died.Codes are as follows:
from QuantLib import *
import matplotlib.pyplot as plt

#global data
stday = 12
stmonth = March
styear = 2017
todaysDate = Date(stday, stmonth, styear)
Settings.instance().evaluationDate = todaysDate
calendar = China()
dayCounter = Actual365Fixed()
settlementDate = todaysDate
riskFreeRate = FlatForward(settlementDate, 0.035, dayCounter)

#option parameters
edday = 28
edmonth = March
edyear = 2017
K = 8
exercise = EuropeanExercise(Date(edday, edmonth, edyear))
payoff = PlainVanillaPayoff(Option.Call, K)

#market data
underlying = SimpleQuote(9)
volatility = BlackConstantVol(todaysDate, calendar, 0.20, dayCounter)
dividendYield = FlatForward(settlementDate, 0.001, dayCounter)


process1 = BlackScholesMertonProcess(QuoteHandle(underlying),
YieldTermStructureHandle(dividendYield),
YieldTermStructureHandle(riskFreeRate),
BlackVolTermStructureHandle(volatility))

process2 = GeneralizedBlackScholesProcess(QuoteHandle(underlying),

YieldTermStructureHandle(dividendYield),

YieldTermStructureHandle(riskFreeRate),

BlackVolTermStructureHandle(volatility))

#asian settings
#try:
averageType = Average().Arithmetic
runningAccumulator = 0
pastFixings = 0
fixingDates = [settlementDate]
option = DiscreteAveragingAsianOption(averageType, runningAccumulator,
pastFixings,
fixingDates,
payoff,
exercise)

stepPerYear = 12
MCstr = 'PseudoRandom'
isBB = True
isAV = True
isCV = True
nrequire = 10000
tolerance = 0.0002
nmax = 15000
seed = 100
seednum = LecuyerUniformRng(1000).next().value()
priceEngine1 = MCDiscreteArithmeticAPEngine(process2, MCstr, isBB, isAV,
isCV, nrequire, tolerance, nmax, seed)
priceEngine2 = MCDiscreteGeometricAPEngine(process2, MCstr, isBB, isAV,
100,0.005, 150, 50)# may need a argument(maxTimeStepsPerYear)
option.setPricingEngine(priceEngine2)
print option.delta()



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[Luigi Ballabio]

Hello,
thanks for bringing this up. There's a couple of things we should fix
with the engine. In the meantime:ut

First, the discrete Asian option calculates the average price (the one that
goes into the payoff) at a number of fixings dates specified by the
contract. The Monte Carlo engine needs at least one of them to be in the
future, otherwise everything is determined and there's no point in doing a
Monte Carlo simulation. However, trying the calculation with missing fixing
dates should raise an exception, not crash the program. We'll try to fix
that in a future release, but in the meantime, passing a sensible list of
dates will cause the calculation to succeed.

Second: depending on whether you use the Arithmetic or Geometric engine
(it's not clear from your example) you'll need a
different runningAccumulator value. The Arithmetic average adds the
fixings, so you need a starting value of 0; the Geometric average
multiplies the fixings, so you need to start from 1 (a 0 will cause the NPV
to be null). This, too, could be improved, meaning that when there's no
past fixings the correct value should be chosen by the engine; but in the
meantime, you can specify it yourself.

Luigi

Post by floatwing
Thank you for your reply first! I am not asking for the next step. I mean
there might be argument errors in the MCDiscreteGeometricAPEngine
function(the arguments the function needs is hard to find in python), event
when i set the fixingDates = [Date(30,12,2017)] for example.By the way, what
does 'fixingDates' mean? I will attatch the new code to the poster, can you
have a check what's wrong to my code?It result in the python kernel
from QuantLib import *
import matplotlib.pyplot as plt
#global data
stday = 12
stmonth = March
styear = 2017
todaysDate = Date(stday, stmonth, styear)
Settings.instance().evaluationDate = todaysDate
calendar = China()
dayCounter = Actual365Fixed()
settlementDate = todaysDate
riskFreeRate = FlatForward(settlementDate, 0.035, dayCounter)
#option parameters
edday = 28
edmonth = March
edyear = 2017
K = 8
exercise = EuropeanExercise(Date(edday, edmonth, edyear))
payoff = PlainVanillaPayoff(Option.Call, K)
#market data
underlying = SimpleQuote(9)
volatility = BlackConstantVol(todaysDate, calendar, 0.20, dayCounter)
dividendYield = FlatForward(settlementDate, 0.001, dayCounter)
process1 = BlackScholesMertonProcess(QuoteHandle(underlying),
YieldTermStructureHandle(dividendYield),
YieldTermStructureHandle(riskFreeRate),
BlackVolTermStructureHandle(volatility))
process2 = GeneralizedBlackScholesProcess(QuoteHandle(underlying),
YieldTermStructureHandle(dividendYield),
YieldTermStructureHandle(riskFreeRate),
BlackVolTermStructureHandle(volatility))
#asian settings
averageType = Average().Arithmetic
runningAccumulator = 0
pastFixings = 0
fixingDates = [settlementDate]
option = DiscreteAveragingAsianOption(averageType, runningAccumulator,
pastFixings,
fixingDates,
payoff,
exercise)
stepPerYear = 12
MCstr = 'PseudoRandom'
isBB = True
isAV = True
isCV = True
nrequire = 10000
tolerance = 0.0002
nmax = 15000
seed = 100
seednum = LecuyerUniformRng(1000).next().value()
priceEngine1 = MCDiscreteArithmeticAPEngine(process2, MCstr, isBB, isAV,
isCV, nrequire, tolerance, nmax, seed)
priceEngine2 = MCDiscreteGeometricAPEngine(process2, MCstr, isBB, isAV,
100,0.005, 150, 50)# may need a argument(maxTimeStepsPerYear)
option.setPricingEngine(priceEngine2)
print option.delta()
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