Re: [Quantlib-users] Bond dirty price different from discounted cashflow?

[Conrad C. <con...@gm...>]

Hi Jian,

The content in this link should provide some clarity to your inquiry.

https://quant.stackexchange.com/questions/12707/pricing-a-fixedratebond-in-quantlib-yield-vs-termstructure/12715#12715
<https://quant.stackexchange.com/questions/12707/pricing-a-fixedratebond-in-quantlib-yield-vs-termstructure/12715#12715>

Regards,

Conrad Cole

https://www.linkedin.com/in/conradcole/
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On 8/13/21 9:52 AM, jian Xu wrote:
> One thing I noticed is that if I set "day_count" to ql.ActualActual()
> instead of ql.ActualActual(ql.ActualActual.ISMA), then the dirty price
> matches the npv exactly.  This is very strange.  The "day_count"
> variable is consistently used in the bond's constructor, dirtyPrice(),
> and InterestRate's constructor.  Why would ql.ActualActual.ISMA
> causing dirty price and the npv to be different?  Am I missing
> something?
>
> On Fri, Aug 13, 2021 at 7:57 AM jian Xu <jia...@gm...> wrote:
>> Hi,
>> I saw some difference between a bond's dirty price and the discounted
>> cashflow to the settlement date.  Cannot figure out why.
>>
>> For example, in the following code, the dirty price is 103.4815, while
>> my discounted cashflow is 103.4674, why?  Thanks a lot.
>>
>> ===============================
>> import QuantLib as ql
>>
>> ## setup the security
>> schedule = ql.MakeSchedule(effectiveDate = ql.Date(30, 6, 2018),
>>                            terminationDate = ql.Date(30, 6, 2023),
>>                            tenor = ql.Period(2),
>>                            calendar =
>> ql.UnitedStates(ql.UnitedStates.GovernmentBond),
>>                            convention = ql.Unadjusted,
>>                            terminalDateConvention=ql.Unadjusted,
>>                            rule = ql.DateGeneration.Backward,
>>                            endOfMonth = True)
>>
>> day_count = ql.ActualActual(ql.ActualActual.ISMA)  # US market
>> convention, not the QuantLib default !!!
>> face = 100
>> redemption = 100
>> issue_date = ql.Date(2, 7, 2018)
>> days_settle = 1
>> coupon = 2.625/100
>> payment_convention = ql.Unadjusted
>> bond = ql.FixedRateBond(days_settle,
>>                         face,
>>                         schedule,
>>                         [coupon],
>>                         day_count,
>>                         payment_convention,
>>                         redemption,
>>                         issue_date)
>>
>> ## Dirty price
>> settle_date = ql.Date(5, 10, 2021)
>> yld = 0.01
>> freq = ql.Semiannual
>> print(bond.dirtyPrice(yld, day_count, ql.Compounded, freq, settle_date))
>>
>> ## my discount cash flow
>> disc = ql.InterestRate(yld, day_count, ql.Compounded, freq)
>> npv = 0
>> for cf in bond.cashflows():
>>     if cf.date() < settle_date:
>>         continue
>>     df = disc.discountFactor(settle_date, cf.date())
>>     npv += cf.amount() * df
>> print(npv)
>
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