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

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Perfect, thank you.

Regards

Philippe Hatstadt
+1-203-252-0408
pha...@ma...
https://www.linkedin.com/in/philippe-hatstadt

> On Jul 14, 2020, at 3:17 AM, Luigi Ballabio <lui...@gm...> wrote:
> 
> 
> 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
>>>> 
>>>> 
>>>> 
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>> 
>> 
>> 
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