Pricing options with holidays

[bgladwyn-pm]

Hi, I'm trying to use Quant lib to price FX options. For some dates, when the settlement date is 2 days after the evaluation, and delivery two days after the expiry I get perfect agreement between bloomberg OVML and quant lib. However, if there is a weekened/holiday between expiry/delivery or evaluation/settlement then there is no longer agreement. How do I get this behavior in quantlib so I can accurately price options?

import QuantLib as ql
import numpy as np

evaluationDate = ql.Date(13, 2, 2018)
settlementDate = evaluationDate + ql.Period(2, ql.Days)  # T+2 = Date(15, Feb, 2018)
expirationDate = ql.Date(13, 2, 2019)  # Date(15, Feb, 2019)
deliveryDate = expirationDate + ql.Period(2, ql.Days)  # Date(19, Feb, 2019)
numberofdays=expirationDate-settlementDate
print(numberofdays)

# Parameters
S = 100
K = 105
f = 0.05  # Foreign rate (EUR in EURUSD)
r = 0.02  # Domestic rate (USD in EURUSD)
vol = 0.2


calendar = ql.UnitedStates(ql.UnitedStates.NYSE)
dayCounter = ql.Actual365Fixed()
exerciseType = ql.Exercise.European
result = 4.6205
tol = 1e-3  # tolerance
optionType = ql.Option.Call
compounding = ql.Compounded
compoundingFrequency = ql.Annual

# Set the evaluation date
ql.Settings.instance().evaluationDate = evaluationDate

# Option data
exercise = ql.EuropeanExercise(expirationDate)
underlyingH = ql.QuoteHandle(ql.SimpleQuote(S))

rTS = ql.YieldTermStructureHandle(ql.FlatForward(evaluationDate, r*365/360, dayCounter, compounding, compoundingFrequency))
fTS = ql.YieldTermStructureHandle(ql.FlatForward(evaluationDate, f*365/360, dayCounter, compounding, compoundingFrequency))
flatVolTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(evaluationDate, calendar, vol, dayCounter))


print(f'Fwd matching bloomberg {1.30*(1+r*365/360)/(1+f*365/360)}')
print(f'Forward rate {1.30*(1+r)/(1+f)}')

payoff = ql.PlainVanillaPayoff(optionType, K)
process = ql.GarmanKohlagenProcess(underlyingH, fTS, rTS, flatVolTS)

option = ql.VanillaOption(payoff, exercise)
engine = ql.AnalyticEuropeanEngine(process)
option.setPricingEngine(engine)

# Calculate option price
calculated = option.NPV()

# Print results
expected = 4.613072
error=(calculated-expected)/expected
print(f"Calculated value = {calculated:.5f}, Expected value = {expected:.5f}, Error = {error*100:.8f}%")

The output matches Bloomberg:

363
Fwd matching bloomberg 1.2623661599471252
Forward rate 1.262857142857143
Calculated value = 4.61307, Expected value = 4.61307, Error = 0.00000739%

But shifting the expiry to 02/15/19 gives:

365
Fwd matching bloomberg 1.2623661599471252
Forward rate 1.262857142857143
Calculated value = 4.62657, Expected value = 4.62016, Error = 0.13883435%

which no longer matches.

Is there a way to consider the correct dates in this calculation?
Thanks for the help! :)

[boring-cyborg]

Thanks for posting! It might take a while before we look at your issue, so don't worry if there seems to be no feedback. We'll get to it.

[github-actions]

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[lballabio]

Hmm—the option is not using settlementDate or deliveryDate for pricing, so there should probably be some correction for that. The option discounts to the evaluation date, and I guess we should discount to the settlement date instead, so something like

calculated /= rTS.discount(settlementDate)

should account for that. In the same way, we're discounting the payoff from the expiration date, not the delivery date, so we should also add

calculated *= rTS.discount(deliveryDate)/rTS.discount(expirationDate)

However, doing that makes the result only slightly better. There might be some other difference—for instance, I see in the second screenshot that r is no longer exactly 5%; is it possible that using that updated rate helps?