Re: [Quantlib-users] European and American valuation

[Brian S. <bri...@gm...>]

Hi, I appreciate any idea if the nearly identical values of American
and European options make sense. Thanks for your input.

On Sat, 3 Oct 2020 at 00:18, Brian Smith <bri...@gm...> wrote:
>
> Hi,
>
> I was performing european and american valuation of the same Swaption
> contract as follows. I found that both NPV values are quite big, and
> they are surprisingly equal. Below is my implementation -
>
> from QuantLib import *
> import datetime
> import numpy as np
> import pandas as pd
>
> calc_date = Date(23, 12, 2013)
> Settings.instance().evaluationDate = calc_date
> spot_dates = [calc_date + Period("1d"), calc_date + Period("2w"),
> calc_date + Period("1m"), calc_date + Period("2m"), calc_date +
> Period("3m"), calc_date + Period("6m"), calc_date + Period("1y"),
> calc_date + Period("2y"), calc_date + Period("3y"), calc_date +
> Period("4y"), calc_date + Period("5y"), calc_date + Period("8y"),
> calc_date + Period("10y"), calc_date + Period("30y")]
> spot_rates = [0.1, 0.13, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.7, 1.4, 1.6, 2, 2, 4]
> us_calendar = UnitedStates()
> zero_curve = ZeroCurve(spot_dates, spot_rates, Actual365Fixed(),
> us_calendar, Linear(), Compounded, Annual)
> termStructure = YieldTermStructureHandle(zero_curve)
> swap = VanillaSwap(VanillaSwap.Payer,
>                       100,
>                       Schedule(Date(1, 12, 2014) + Period("6m"),
> Date(1, 12, 2019), Period(6, Months), us_calendar, Unadjusted,
> Unadjusted, DateGeneration.Forward, False),
>                       3/100,
>                       Thirty360(Thirty360.BondBasis),
>                       Schedule(Date(1, 12, 2014) + Period("6m"),
> Date(1, 12, 2019), Period(6, Months), us_calendar, Unadjusted,
> Unadjusted, DateGeneration.Forward, False),
>                       USDLibor(Period(6, Months), termStructure),
>                       0.0,
>                       USDLibor(Period(6, Months), termStructure).dayCounter()
>                     )
>
> exercised = EuropeanExercise(Date(1, 12, 2014))
> atmswaption = Swaption(swap, exercised)
> atmswaption.setPricingEngine(TreeSwaptionEngine(BlackKarasinski(termStructure),
> 3000)); print(atmswaption.NPV())
>
> exercised = AmericanExercise(Date(1, 3, 2014), Date(1, 12, 2014))
> atmswaption = Swaption(swap, exercised)
> atmswaption.setPricingEngine(TreeSwaptionEngine(BlackKarasinski(termStructure),
> 3000)); print(atmswaption.NPV())
>
> Is there any reason why they are so close? Your pointer will be very helpful.
>
> Many thanks,