Re: [Quantlib-users] Swap floating cash flows with negative fwd rates seem wrong

SourceForge Headquarters 1320 Columbia Street Suite 310 San Diego, CA 92101 +1 (858) 422-6466

If you create your index as:

    RelinkableHandle<YieldTermStructure> forecastHandle;
    forecastHandle.linkTo(originalCurve);
    ext::shared_ptr<IborIndex> index =
ext::make_shared<Euribor6M>(forecastHandle) // for instance: works with any
floating index

or the equivalent in Python:

    forecastHandle = RelinkableYieldTermStructureHandle()
    forecastHandle.linkTo(originalCurve)
    index = Euribor6M(forecastHandle)

then, when you link the handle to a different curve with

    forecastHandle.linkTo(newCurve);

the index will start using the new one for forecasting.  If you used the
index to build a swap, the swap will start using the new curve too.

Luigi

On Tue, Jul 14, 2020 at 2:30 AM Philippe Hatstadt <
phi...@ex...> wrote:

> I think I know what is wrong. I do not set the floating rate index to be
> generated from each Hull-White curve but from the original curve, that has
> positive rates.
> So the question simply is this: Is there a way to change the curve used to
> generate the floating index in a swap, or is the only way to re-instantiate
> a new swap based on an index pointing to my path-dependent curve?
> I'd rather change the index and keep the same instance of my swap, but
> maybe that's not possible? Stated differently, is there the equivalent of a
> pricing engine for the floating index forecasting?
>
> Regards
>
> Philippe
>
>
> On Mon, Jul 13, 2020 at 5:56 AM Amine Ifri <ami...@gm...> wrote:
>
>> I use the C++ library and never had an issue with swap.fairRate(). It
>> gives me positive as well as negative values depending on the term
>> structures.
>>
>> As far as checking the CPP code, it looks correct to me. Do you mind
>> sharing the swap details you are trying to price/simulate?
>>
>> Amine
>>
>> On 12 Jul 2020, at 03:02, Philippe Hatstadt <
>> phi...@ex...> wrote:
>>
>> I'm using a Hull-White model to generate forward paths of the short rate,
>> from which I then build a discounting curve, from which I compute forward
>> swap values towards Monte-carlo integration of certain path dependent swap
>> rate linked derivatives. Here, I am looking at a 2y into 10y swaption, and
>> for each path, I want to calculate the forward swap rate and the swap NPV.
>> My problem is that I have a curve that has negative rates on a certain
>> path, the 2y into 10y forward swap.fairRate() function returns like 94bp.
>> Since all rates are negative, it's pretty clear that fairRate() should be
>> negative, and if I use the curve's discount factors and use the good old
>> approximation for the swap rate with the formula C/2 *
>> Sum_i(FixedLegDiscountFactor(i))/(1-DiscountFactor(TMat)) then I get the
>> correct -250bp forward swap rate (where i=1 to 20 corresponding to 20
>> forward semi-annual fixed payments).
>> So I am wondering if the swap cash flows do not work with negative rates
>> or else, but as it stands right now, the swap.fairRate() function doesn't
>> work at all. I also checked that by solving for the fixed rate that would
>> make the swap net cash-flows to be equal to zero, then I get the value
>> returned by swap.fairRate(). This would further indicate that the latter
>> function is correct, but that the cash flows are not. lastly, whether I
>> select a path with positive or negative forward rates, the cf.amount() is
>> always positive.
>> This is the code I use to generate the cash-flows:
>>
>> def swap_cash_flows(swap: ql.Swap,
>>                     crvh,
>>                     ):
>>     output_list = []
>>     for i, cf in enumerate(swap.leg(0)):
>>         dt = cf.date()
>>         dfact = crvh.discount(dt)
>>         output_list.append(['leg0', cf.date(), dfact, cf.amount()])
>>     for i, cf in enumerate(swap.leg(1)):
>>         dt = cf.date()
>>         dfact = crvh.discount(dt)
>>         output_list.append(['leg1', cf.date(), dfact, cf.amount()])
>>     df1 = pd.DataFrame(columns=['leg', 'cf_date', 'disc_fact', 'cf_amount'], data=output_list)
>>     return df1
>>
>> The short-rate path corresponding to the curve handle crvh is as follows:
>> <image.png>
>> and lastly, this is the table of cash flows, dates and discount factors:
>> leg cf_date disc_fact cf_amount
>> leg0 2023-01-11 1.031727084 0.004717496
>> leg0 2023-07-11 1.044326706 0.004640581
>> leg0 2024-01-11 1.056475309 0.004717496
>> leg0 2024-07-11 1.067323978 0.004666219
>> leg0 2025-01-13 1.080208917 0.004768773
>> leg0 2025-07-11 1.095773345 0.004589303
>> leg0 2026-01-12 1.107358267 0.004743135
>> leg0 2026-07-13 1.119706713 0.004666219
>> leg0 2027-01-11 1.134937064 0.004666219
>> leg0 2027-07-12 1.148588556 0.004666219
>> leg0 2028-01-11 1.164662739 0.004691858
>> leg0 2028-07-11 1.184811281 0.004666219
>> leg0 2029-01-11 1.202933688 0.004717496
>> leg0 2029-07-11 1.22143445 0.004640581
>> leg0 2030-01-11 1.244698418 0.004717496
>> leg0 2030-07-11 1.268437607 0.004640581
>> leg0 2031-01-13 1.289269217 0.004768773
>> leg0 2031-07-11 1.310335034 0.004589303
>> leg0 2032-01-12 1.330460609 0.004743135
>> leg0 2032-07-12 1.351119197 0.004666219
>> leg1 2022-10-11 1.025077227 0.000595151
>> leg1 2023-01-11 1.031727084 0.000595151
>> leg1 2023-04-11 1.037740592 0.000582209
>> leg1 2023-07-11 1.044326706 0.00058868
>> leg1 2023-10-11 1.050712784 0.001151809
>> leg1 2024-01-11 1.056475309 0.001190658
>> leg1 2024-04-11 1.062040699 0.001177708
>> leg1 2024-07-11 1.067323978 0.001177708
>> leg1 2024-10-11 1.073341181 0.001190658
>> leg1 2025-01-13 1.080208917 0.001216557
>> leg1 2025-04-11 1.087963402 0.00113886
>> leg1 2025-07-11 1.095773345 0.001322081
>> leg1 2025-10-14 1.102080743 0.002477114
>> leg1 2026-01-12 1.107358267 0.002346587
>> leg1 2026-04-13 1.112978456 0.002372691
>> leg1 2026-07-13 1.119706713 0.002372691
>> leg1 2026-10-13 1.127732208 0.002398796
>> leg1 2027-01-11 1.134937064 0.002346587
>> leg1 2027-04-12 1.141923849 0.002372691
>> leg1 2027-07-12 1.148588556 0.002390753
>> leg1 2027-10-12 1.155929127 0.002537285
>> leg1 2028-01-11 1.164662739 0.002509671
>> leg1 2028-04-11 1.174741361 0.002509671
>> leg1 2028-07-11 1.184811281 0.002509671
>> leg1 2028-10-11 1.194083437 0.002537285
>> leg1 2029-01-11 1.202933688 0.002537285
>> leg1 2029-04-11 1.211815927 0.002482058
>> leg1 2029-07-11 1.22143445 0.002509671
>> leg1 2029-10-11 1.232822712 0.002537285
>> leg1 2030-01-11 1.244698418 0.002537285
>> leg1 2030-04-11 1.256926582 0.002482058
>> leg1 2030-07-11 1.268437607 0.003472659
>> leg1 2030-10-11 1.278474854 0.004092082
>> leg1 2031-01-13 1.289269217 0.004181226
>> leg1 2031-04-11 1.299839855 0.003914165
>> leg1 2031-07-11 1.310335034 0.004047153
>> leg1 2031-10-14 1.320633529 0.004225801
>> leg1 2032-01-12 1.330460609 0.004002946
>> leg1 2032-04-12 1.340898895 0.004047513
>> leg1 2032-07-12 1.351119197 0.004047513
>> Regards
>>
>> Philippe
>>
>>
>>
>> Brokerage services offered through Exos Securities LLC, member of SIPC
>> <http://www.sipc.org/> / FINRA <http://www.finra.org/>. For important
>> disclosures, click here <https://www.exosfinancial.com/disclosures>.
>> _______________________________________________
>> QuantLib-users mailing list
>> Qua...@li...
>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>>
>>
>>
>
>
> Brokerage services offered through Exos Securities LLC, member of SIPC
> <http://www.sipc.org/> / FINRA <http://www.finra.org/>. For important
> disclosures, click here <https://www.exosfinancial.com/disclosures>.
> _______________________________________________
> QuantLib-users mailing list
> Qua...@li...
> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>