Product¶

MCQuantLib provides many options types as default pricing models. This chapter is to show how to use them.

Import¶

You should always import stochastic process module and monte carlo engine module before any pricing:

from MCQuantLib import Engine, BlackScholes, Heston
batchSize = 100
numIteration = 900
r = 0.03
q = 0
v = 0.25
dayCounter = 252
mc = Engine(batchSize, numIteration)
bs = BlackScholes(r, q, v, dayCounter)

Name Convention¶

MCQuantLib supports coding by two kinds of style, one is called as Academy Style and another is called as QuantLib Style. The difference between them is the Academy Style coding uses array and pure number to represent dates, while QuantLib Style uses calendar and pandas.Timestamp to mark dates.

To use Academy Style, you should import the class with Option suffix, such as VanillaCallOption and UpOutOption. To use QuantLib Style, you should import the class without Option suffix, such as VanillaCall and UpOut.

Vanilla Call Option¶

To price a vanilla Call Option, use:

from MCQuantLib import VanillaCallOption
option = VanillaCallOption(
    spot=100,
    observationDay=np.linspace(1, 252, 252),
    strike=100
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import VanillaCall, Calendar
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
observationDate = calendar.makeScheduleByPeriod(start, '1d', 253, True)[1:]
option = VanillaCall(start, observationDate, strike=100, calendar=calendar)
option.value(start, 100, mc, bs)

Vanilla Put Option¶

To price a vanilla Put Option, use:

from MCQuantLib import VanillaPutOption
option = VanillaPutOption(
    spot=100,
    observationDay=np.linspace(1, 252, 252),
    strike=100
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import VanillaPut, Calendar
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
observationDate = calendar.makeScheduleByPeriod(start, '1d', 253, True)[1:]
option = VanillaPut(start, observationDate, strike=100, calendar=calendar)
option.value(start, 100, mc, bs)

Barrier Option¶

Barrier Option in MCQuantLib is different with those in QuantLib, even they may have the same name. All Barrier Options in QuantLib are continuously observed, while barrier options in MCQuantLib are all discretely observed. For knock-out options, discretely observed option usually has higher price than continuously observed ones. For knock-in options, discretely observed option usually has lower price than continuously observed ones.

Up-Out Option¶

To price a vanilla Up-Out Barrier Option, use:

from MCQuantLib import UpOutOption, PlainVanillaPayoff
option = UpOutOption(
    spot=100,
    barrier=120,
    rebate=0,
    observationDay=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1, strike=100)
)
option.calculateValue(mc, bs, requestGreek=True)

For time-varying barrier and rebate, pass in an array to barrier:

from MCQuantLib import UpOutOption, PlainVanillaPayoff
optionTimeVaryingBarrier = UpOutOption(
    spot=100,
    barrier=np.linspace(110, 120, 252),
    rebate=np.linspace(0, 3, 252),
    observationDay=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1, strike=100)
)
optionTimeVaryingBarrier.calculateValue(mc, bs)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import UpOut, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockOutObservationDate = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
option = UpOut(start, 120, 10, knockOutObservationDate, payoff=PlainVanillaPayoff(strike=100, optionType=1),calendar=calendar)
option.value(start, 100, mc, bs)

Up-In Option¶

To price a vanilla Up-In Barrier Option, use:

from MCQuantLib import UpInOption, PlainVanillaPayoff
option = UpInOption(
    spot=100,
    barrier=120,
    rebate=0,
    observationDay=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1,strike=100)
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import UpIn, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockOutObservationDate = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
option = UpIn(start, 120, 10, knockOutObservationDate, payoff=-PlainVanillaPayoff(strike=100, optionType=-1),calendar=calendar)
option.value(start, 100, mc, bs)

Down-Out Option¶

To price a vanilla Down-Out Barrier Option, use:

from MCQuantLib import DownOutOption, PlainVanillaPayoff
option = DownOutOption(
    spot=100,
    barrier=80,
    rebate=0,
    observationDay=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1, strike=100)
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import DownOut, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockOutObservationDate = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
option = DownOut(start, 87, 10, knockOutObservationDate, payoff=PlainVanillaPayoff(strike=100, optionType=-1),calendar=calendar)
option.value(start, 100, mc, bs)

Down-In Option¶

To price a vanilla Down-In Barrier Option, use:

from MCQuantLib import DownInOption, PlainVanillaPayoff
option = DownInOption(
    spot=100,
    barrier=80,
    rebate=0,
    observationDay=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1, strike=100)
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import DownIn, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockOutObservationDate = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
option = DownIn(start, 87, 10, knockOutObservationDate, payoff=-PlainVanillaPayoff(strike=100, optionType=-1),calendar=calendar)
option.value(start, 100, mc, bs)

Double-Out Option¶

To price a vanilla Double-Out Barrier Option, use:

from MCQuantLib import DoubleOutOption, PlainVanillaPayoff
option = DoubleOutOption(
    spot=100,
    barrierUp=120,
    barrierDown=80,
    observationDayUp=np.linspace(1, 252, 252),
    observationDayDown=np.linspace(1, 252, 252),
    payoff=PlainVanillaPayoff(optionType=1, strike=100),
    rebateUp=1,
    rebateDown=2
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import DoubleOut, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockOutObservationDateUp = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
knockOutObservationDateDown = calendar.makeScheduleByPeriod(start, '2M', 7, True)[1:]
option = DoubleOut(
    spot=100,
    barrierUp=120,
    barrierDown=80,
    observationDayUp=knockOutObservationDateUp,
    observationDayDown=knockOutObservationDateDown,
    payoff=PlainVanillaPayoff(strike=100, optionType=1),
    rebateUp=3,
    rebateDown=2
)
option.value(start, 100, mc, bs)

Double-In Option¶

To price a vanilla Double-In Barrier Option, use:

from MCQuantLib import DoubleInOption, PlainVanillaPayoff
option = DoubleInOption(
    spot=100,
    barrierUp=120,
    barrierDown=80,
    observationDayUp=np.linspace(1, 252, 21),
    observationDayDown=np.linspace(1, 252, 252),
    rebate=2,
    payoff=PlainVanillaPayoff(optionType=1, strike=100)
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import DoubleIn, Calendar, PlainVanillaPayoff
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
knockInObservationDateUp = calendar.makeScheduleByPeriod(start, '1M', 13, True)[1:]
knockInObservationDateDown = calendar.makeScheduleByPeriod(start, '2M', 7, True)[1:]
option = DoubleIn(
    spot=100,
    barrierUp=120,
    barrierDown=80,
    observationDayUp=knockInObservationDateUp,
    observationDayDown=knockInObservationDateDown,
    payoff=PlainVanillaPayoff(strike=100, optionType=1),
    rebateUp=3,
    rebateDown=2
)
option.value(start, 100, mc, bs)

SnowBall Option¶

To price a Snow Ball Option, use:

from MCQuantLib import SnowBallOption
option = SnowBallOption(
    spot=100,
    upperBarrierOut=105,
    lowerBarrierIn=80,
    observationDayIn=np.linspace(1, 252, 252),
    observationDayOut=np.linspace(1, 252, 12),
    rebateOut=np.linspace(1, 15, 12),
    fullCoupon=15
)
option.calculateValue(mc, bs, requestGreek=True)

If you prefer a QuantLib Style and want to use calendar object:

import pandas as pd
import QuantLib as ql
from MCQuantLib import SnowBall, PlainVanillaPayoff, Calendar
calendar = Calendar(ql.Japan())
start = pd.Timestamp(2024, 7, 9)
assert calendar.isTrading(start)
monthlyDates = calendar.makeScheduleByPeriod(start, "1m", 13)[1:]
shortPut = - PlainVanillaPayoff(optionType=-1, strike=100)
option = SnowBall(
    startDate=start, initialPrice=100, knockOutBarrier=105,
    knockOutObservationDate=monthlyDates, knockInBarrier=80, knockInObservationDate="daily",
    knockInPayoff=shortPut, knockOutCouponRate=0.15,
    maturityCouponRate=0.15, calendar=calendar
)
option.value(pd.Timestamp(2024, 8, 8), 102, False, mc, bs)

Product¶

Import¶

Name Convention¶

Vanilla Call Option¶

Vanilla Put Option¶

Barrier Option¶

Up-Out Option¶

Up-In Option¶

Down-Out Option¶

Down-In Option¶

Double-Out Option¶

Double-In Option¶

SnowBall Option¶

MCQuantLib

Navigation

Related Topics