Pricing options with holidays

[bgladwyn-pm]

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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, r365/360, dayCounter, compounding, compoundingFrequency)) fTS = ql.YieldTermStructureHandle(ql.FlatForward(evaluationDate, f365/360, dayCounter, compounding, compoundingFrequency)) flatVolTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(evaluationDate, calendar, vol, dayCounter))

print(f'Fwd matching bloomberg {1.30*(1+r365/360)/(1+f365/360)}') 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! :)

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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?

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This issue was automatically marked as stale because it has been open 60 days with no activity. Remove stale label or comment, or this will be closed in two weeks.

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This issue was automatically closed because it has been stalled for two weeks with no further activity.