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

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It’s the underlying swap of a swaption. US curve. Swap starts in 2y and ends in 12y. Semi annual fixed act/act versus USDLibor 3M floating a/360.
The Hull White path is harder to share other than by providing daily discount factors.
Defining dfs and dfe as the discount factors at 2y and 12y, I was able to get the correct fairRate manually by stating that floating leg NPV is equal to dfs - dfe. swap.fixedLegNPV() is correct but not swap.flioatingLeg.NPV().
I used today as evaluation date.
As you can see below, the floating leg cash flow amounts never change in sign even when the forward rate does. I realize my graph is the instantaneous forward, but the 3M can easily be calculated from the discount factors.

Regards

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

> On Jul 13, 2020, at 5:57 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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