Cross-currency basis swap pricing

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Cross-currency basis swap pricing

Kirill Shemyakin
Hi all,

Does anybody know whether it is possible to price a plain vanilla
floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
using quantlib. Does quantlib also possess functionality to build
curves needed (one for EUR based on EONIA, one for USD based on Fed
Funds Rate and cross-currency)?

Many thanks in advance!

Best regards,
Kirill

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Re: Cross-currency basis swap pricing

Luigi Ballabio
Hi,
   EONIA curve building is supported by the OISRateHelper class. I'm
not sure that this can be applied to Fed Funds.  However, the
showstopper might be the the cross-currency feature. I'm not sure that
you can manage the fact that the two legs are in different currencies
(if the legs are not readjusting, you might do it by converting the
notional with the current FX rate, I guess; but otherwise, you're out
of luck).

Luigi


On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:

> Hi all,
>
> Does anybody know whether it is possible to price a plain vanilla
> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
> using quantlib. Does quantlib also possess functionality to build
> curves needed (one for EUR based on EONIA, one for USD based on Fed
> Funds Rate and cross-currency)?
>
> Many thanks in advance!
>
> Best regards,
> Kirill
>
> ------------------------------------------------------------------------------
> Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS,
> MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current
> with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft
> MVPs and experts. ON SALE this month only -- learn more at:
> http://p.sf.net/sfu/learnnow-d2d
> _______________________________________________
> QuantLib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users

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R: Cross-currency basis swap pricing

Ballabio Gerardo-4
I've built a Fed Funds curve using OISRateHelper (in QuantLibXL) and it seems to work fine (it is almost identical to the curve built by Murex).

Gerardo


-----Messaggio originale-----
Da: Luigi Ballabio [mailto:[hidden email]]
Inviato: mercoledì 6 febbraio 2013 10.15
A: Kirill Shemyakin
Cc: quantlib-users
Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing

Hi,
   EONIA curve building is supported by the OISRateHelper class. I'm not sure that this can be applied to Fed Funds.  However, the showstopper might be the the cross-currency feature. I'm not sure that you can manage the fact that the two legs are in different currencies (if the legs are not readjusting, you might do it by converting the notional with the current FX rate, I guess; but otherwise, you're out of luck).

Luigi


On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:

> Hi all,
>
> Does anybody know whether it is possible to price a plain vanilla
> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
> using quantlib. Does quantlib also possess functionality to build
> curves needed (one for EUR based on EONIA, one for USD based on Fed
> Funds Rate and cross-currency)?
>
> Many thanks in advance!
>
> Best regards,
> Kirill
>
> ----------------------------------------------------------------------
> -------- Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012,
> HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your
> skills current with LearnDevNow - 3,200 step-by-step video tutorials
> by Microsoft MVPs and experts. ON SALE this month only -- learn more
> at:
> http://p.sf.net/sfu/learnnow-d2d
> _______________________________________________
> QuantLib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users

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Re: Cross-currency basis swap pricing

Luigi Ballabio
Ok, thanks.  There's still the currency conversion to be taken care
of, though...

On Wed, Feb 6, 2013 at 12:15 PM, Ballabio Gerardo
<[hidden email]> wrote:

> I've built a Fed Funds curve using OISRateHelper (in QuantLibXL) and it seems to work fine (it is almost identical to the curve built by Murex).
>
> Gerardo
>
>
> -----Messaggio originale-----
> Da: Luigi Ballabio [mailto:[hidden email]]
> Inviato: mercoledì 6 febbraio 2013 10.15
> A: Kirill Shemyakin
> Cc: quantlib-users
> Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing
>
> Hi,
>    EONIA curve building is supported by the OISRateHelper class. I'm not sure that this can be applied to Fed Funds.  However, the showstopper might be the the cross-currency feature. I'm not sure that you can manage the fact that the two legs are in different currencies (if the legs are not readjusting, you might do it by converting the notional with the current FX rate, I guess; but otherwise, you're out of luck).
>
> Luigi
>
>
> On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:
>> Hi all,
>>
>> Does anybody know whether it is possible to price a plain vanilla
>> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
>> using quantlib. Does quantlib also possess functionality to build
>> curves needed (one for EUR based on EONIA, one for USD based on Fed
>> Funds Rate and cross-currency)?
>>
>> Many thanks in advance!
>>
>> Best regards,
>> Kirill
>>
>> ----------------------------------------------------------------------
>> -------- Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012,
>> HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your
>> skills current with LearnDevNow - 3,200 step-by-step video tutorials
>> by Microsoft MVPs and experts. ON SALE this month only -- learn more
>> at:
>> http://p.sf.net/sfu/learnnow-d2d
>> _______________________________________________
>> QuantLib-users mailing list
>> [hidden email]
>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>
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> Banca Profilo S.p.A.
> Corso Italia, 49 - 20122 Milano - Tel. 02 58408.1, Fax 02 5831 6057
> Capitale Sociale Euro 136.794.106,00 i.v.
> Iscrizione al Registro Imprese di Milano, C.F. e P.IVA 09108700155 - [hidden email]
> Iscritta all’Albo delle Banche e dei Gruppi bancari
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>
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> DISCLAIMER:
> The information transmitted may contain confidential and/or privileged material.
> Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon,
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Re: Cross-currency basis swap pricing

Peter Caspers-4
Gerardo, may I ask something. I know of direct Fed Fund swap quotes up
to two years. For longer maturities there are basis swaps Fed Fund vs.
Libor, so stripping the Fed Fund curve requires then simultaneous
stripping of the Fed Fund curve and the Libor forward curve (the latter
with Fed Fund discounting), is that correct? Murex is able to do such a
kind of calibration, but ql seems to require some modification for this.
How did you handle this ?
Thank you, Peter

Am 06.02.2013 12:30, schrieb Luigi Ballabio:

> Ok, thanks.  There's still the currency conversion to be taken care
> of, though...
>
> On Wed, Feb 6, 2013 at 12:15 PM, Ballabio Gerardo
> <[hidden email]> wrote:
>> I've built a Fed Funds curve using OISRateHelper (in QuantLibXL) and it seems to work fine (it is almost identical to the curve built by Murex).
>>
>> Gerardo
>>
>>
>> -----Messaggio originale-----
>> Da: Luigi Ballabio [mailto:[hidden email]]
>> Inviato: mercoledì 6 febbraio 2013 10.15
>> A: Kirill Shemyakin
>> Cc: quantlib-users
>> Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing
>>
>> Hi,
>>     EONIA curve building is supported by the OISRateHelper class. I'm not sure that this can be applied to Fed Funds.  However, the showstopper might be the the cross-currency feature. I'm not sure that you can manage the fact that the two legs are in different currencies (if the legs are not readjusting, you might do it by converting the notional with the current FX rate, I guess; but otherwise, you're out of luck).
>>
>> Luigi
>>
>>
>> On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:
>>> Hi all,
>>>
>>> Does anybody know whether it is possible to price a plain vanilla
>>> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
>>> using quantlib. Does quantlib also possess functionality to build
>>> curves needed (one for EUR based on EONIA, one for USD based on Fed
>>> Funds Rate and cross-currency)?
>>>
>>> Many thanks in advance!
>>>
>>> Best regards,
>>> Kirill
>>>
>>> ----------------------------------------------------------------------
>>> -------- Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012,
>>> HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your
>>> skills current with LearnDevNow - 3,200 step-by-step video tutorials
>>> by Microsoft MVPs and experts. ON SALE this month only -- learn more
>>> at:
>>> http://p.sf.net/sfu/learnnow-d2d
>>> _______________________________________________
>>> QuantLib-users mailing list
>>> [hidden email]
>>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>> ------------------------------------------------------------------------------
>> Free Next-Gen Firewall Hardware Offer
>> Buy your Sophos next-gen firewall before the end March 2013 and get the hardware for free! Learn more.
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>> _______________________________________________
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>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
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>> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
>> <html xmlns="http://www.w3.org/1999/xhtml">
>> <head></head>
>> <body>
>> <div style="font-family:Calibri;font-size:10px">
>> Banca Profilo S.p.A.
>> Corso Italia, 49 - 20122 Milano - Tel. 02 58408.1, Fax 02 5831 6057
>> Capitale Sociale Euro 136.794.106,00 i.v.
>> Iscrizione al Registro Imprese di Milano, C.F. e P.IVA 09108700155 - [hidden email]
>> Iscritta all’Albo delle Banche e dei Gruppi bancari
>> Aderente al Fondo Interbancario di Tutela dei depositi
>> Aderente al Conciliatore Bancario Finanziario e all’Arbitro Bancario Finanziario
>> Appartenente al Gruppo bancario Banca Profilo e soggetta all’attività di direzione e coordinamento di Arepo BP S.p.A.
>>
>>
>> DISCLAIMER:
>> The information transmitted may contain confidential and/or privileged material.
>> Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon,
>> this information by persons or entities other than the intended recipient is prohibited.
>> If you received this in error, please contact the sender and delete the material from any computer.
>> </div>
>> </body>
>> </html>
>>
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> and get the hardware for free! Learn more.
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R: Cross-currency basis swap pricing

Ballabio Gerardo-4
Bloomberg currently quotes Fed Funds swaps with maturities up to 40 years. Their codes are of the form "USSO* Curncy" (that's a letter O, not a zero) where you replace the * with the usual Bloomberg scheme for maturities, i.e., "USSO1Z Curncy" for 1 week, "USSOC Curncy" for 3 months, "USSO10 Curncy" for 10 years, and so on. I'm simply using those.

Still, if you need to use a "compounded" quote (as would be Fed Funds swaps obtained as Libor + Fed Funds-Libor basis), I'd suggest that you create the associated RateHelper just as you normally do, and then feed it with the sum of the two quotes. You may use a CompositeQuote for that.

Gerardo

-----Messaggio originale-----
Da: Peter Caspers [mailto:[hidden email]]
Inviato: giovedì 7 febbraio 2013 20.21
A: Luigi Ballabio
Cc: Ballabio Gerardo; quantlib-users
Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing

Gerardo, may I ask something. I know of direct Fed Fund swap quotes up to two years. For longer maturities there are basis swaps Fed Fund vs.
Libor, so stripping the Fed Fund curve requires then simultaneous stripping of the Fed Fund curve and the Libor forward curve (the latter with Fed Fund discounting), is that correct? Murex is able to do such a kind of calibration, but ql seems to require some modification for this.
How did you handle this ?
Thank you, Peter

Am 06.02.2013 12:30, schrieb Luigi Ballabio:

> Ok, thanks.  There's still the currency conversion to be taken care
> of, though...
>
> On Wed, Feb 6, 2013 at 12:15 PM, Ballabio Gerardo
> <[hidden email]> wrote:
>> I've built a Fed Funds curve using OISRateHelper (in QuantLibXL) and it seems to work fine (it is almost identical to the curve built by Murex).
>>
>> Gerardo
>>
>>
>> -----Messaggio originale-----
>> Da: Luigi Ballabio [mailto:[hidden email]]
>> Inviato: mercoledì 6 febbraio 2013 10.15
>> A: Kirill Shemyakin
>> Cc: quantlib-users
>> Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing
>>
>> Hi,
>>     EONIA curve building is supported by the OISRateHelper class. I'm not sure that this can be applied to Fed Funds.  However, the showstopper might be the the cross-currency feature. I'm not sure that you can manage the fact that the two legs are in different currencies (if the legs are not readjusting, you might do it by converting the notional with the current FX rate, I guess; but otherwise, you're out of luck).
>>
>> Luigi
>>
>>
>> On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:
>>> Hi all,
>>>
>>> Does anybody know whether it is possible to price a plain vanilla
>>> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
>>> using quantlib. Does quantlib also possess functionality to build
>>> curves needed (one for EUR based on EONIA, one for USD based on Fed
>>> Funds Rate and cross-currency)?
>>>
>>> Many thanks in advance!
>>>
>>> Best regards,
>>> Kirill
>>>
>>> --------------------------------------------------------------------
>>> --
>>> -------- Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012,
>>> HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your
>>> skills current with LearnDevNow - 3,200 step-by-step video tutorials
>>> by Microsoft MVPs and experts. ON SALE this month only -- learn more
>>> at:
>>> http://p.sf.net/sfu/learnnow-d2d
>>> _______________________________________________
>>> QuantLib-users mailing list
>>> [hidden email]
>>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>> ---------------------------------------------------------------------
>> --------- Free Next-Gen Firewall Hardware Offer Buy your Sophos
>> next-gen firewall before the end March 2013 and get the hardware for free! Learn more.
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>>
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>> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
>> <html xmlns="http://www.w3.org/1999/xhtml">
>> <head></head>
>> <body>
>> <div style="font-family:Calibri;font-size:10px">
>> Banca Profilo S.p.A.
>> Corso Italia, 49 - 20122 Milano - Tel. 02 58408.1, Fax 02 5831 6057
>> Capitale Sociale Euro 136.794.106,00 i.v.
>> Iscrizione al Registro Imprese di Milano, C.F. e P.IVA 09108700155 -
>> [hidden email] Iscritta all'Albo delle Banche e dei Gruppi
>> bancari Aderente al Fondo Interbancario di Tutela dei depositi
>> Aderente al Conciliatore Bancario Finanziario e all'Arbitro Bancario
>> Finanziario Appartenente al Gruppo bancario Banca Profilo e soggetta all'attività di direzione e coordinamento di Arepo BP S.p.A.
>>
>>
>> DISCLAIMER:
>> The information transmitted may contain confidential and/or privileged material.
>> Any review, retransmission, dissemination or other use of, or taking
>> of any action in reliance upon, this information by persons or entities other than the intended recipient is prohibited.
>> If you received this in error, please contact the sender and delete the material from any computer.
>> </div>
>> </body>
>> </html>
>>
> ----------------------------------------------------------------------
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> Buy your Sophos next-gen firewall before the end March 2013 and get
> the hardware for free! Learn more.
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Iscritta all’Albo delle Banche e dei Gruppi bancari
Aderente al Fondo Interbancario di Tutela dei depositi
Aderente al Conciliatore Bancario Finanziario e all’Arbitro Bancario Finanziario
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Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon,
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Re: R: Cross-currency basis swap pricing

Francis Duffy
Hi all,

There is the added complication that the Fed Funds leg of the basis swap is an arithmetic average and not daily compounded like in the case of the straight OIS swaps. I do not think that this is handled by QuantLib either.

For it's USD OIS curve, Bloomberg uses an approximation from 7Y out where it uses the Fed Funds basis swap spreads and standard USD IRS to create an approximate swap against 3M USD Libor. They provide a document describing the approximation.

I don't think that simultaneous bootstrapping is necessary here though. If you combine the Fed Fund basis swap with the standard USD swap, the 3M USD Libor legs cancel and you are left with a swap of a semi-annual 30/360 fixed rate against (arithmetic average) quarterly ACT/360 Fed Funds plus spread that should have value 0. The only unknown here is the OIS discount factor and you only need a 1D bootstrap.

To allow this in QuantLib, I think that you would need to create an arithmetic average OIS swap instrument and a RateHelper for it (that allows a spread on the index leg). To increase speed of computation on the arithmetic average leg (i.e. to avoid calculating the daily forwards), the paper "Valuation of Arithmetic Average of Fed Funds Rates and Construction of the US dollar Swap Yield Curve" by Takada has a good approximation.

Thanks,
Francis.

On Fri, Feb 8, 2013 at 8:29 AM, Ballabio Gerardo <[hidden email]> wrote:
Bloomberg currently quotes Fed Funds swaps with maturities up to 40 years. Their codes are of the form "USSO* Curncy" (that's a letter O, not a zero) where you replace the * with the usual Bloomberg scheme for maturities, i.e., "USSO1Z Curncy" for 1 week, "USSOC Curncy" for 3 months, "USSO10 Curncy" for 10 years, and so on. I'm simply using those.

Still, if you need to use a "compounded" quote (as would be Fed Funds swaps obtained as Libor + Fed Funds-Libor basis), I'd suggest that you create the associated RateHelper just as you normally do, and then feed it with the sum of the two quotes. You may use a CompositeQuote for that.

Gerardo

-----Messaggio originale-----
Da: Peter Caspers [mailto:[hidden email]]
Inviato: giovedì 7 febbraio 2013 20.21
A: Luigi Ballabio
Cc: Ballabio Gerardo; quantlib-users
Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing

Gerardo, may I ask something. I know of direct Fed Fund swap quotes up to two years. For longer maturities there are basis swaps Fed Fund vs.
Libor, so stripping the Fed Fund curve requires then simultaneous stripping of the Fed Fund curve and the Libor forward curve (the latter with Fed Fund discounting), is that correct? Murex is able to do such a kind of calibration, but ql seems to require some modification for this.
How did you handle this ?
Thank you, Peter

Am 06.02.2013 12:30, schrieb Luigi Ballabio:
> Ok, thanks.  There's still the currency conversion to be taken care
> of, though...
>
> On Wed, Feb 6, 2013 at 12:15 PM, Ballabio Gerardo
> <[hidden email]> wrote:
>> I've built a Fed Funds curve using OISRateHelper (in QuantLibXL) and it seems to work fine (it is almost identical to the curve built by Murex).
>>
>> Gerardo
>>
>>
>> -----Messaggio originale-----
>> Da: Luigi Ballabio [mailto:[hidden email]]
>> Inviato: mercoledì 6 febbraio 2013 10.15
>> A: Kirill Shemyakin
>> Cc: quantlib-users
>> Oggetto: Re: [Quantlib-users] Cross-currency basis swap pricing
>>
>> Hi,
>>     EONIA curve building is supported by the OISRateHelper class. I'm not sure that this can be applied to Fed Funds.  However, the showstopper might be the the cross-currency feature. I'm not sure that you can manage the fact that the two legs are in different currencies (if the legs are not readjusting, you might do it by converting the notional with the current FX rate, I guess; but otherwise, you're out of luck).
>>
>> Luigi
>>
>>
>> On Thu, Jan 24, 2013 at 9:38 PM, Kirill Shemyakin <[hidden email]> wrote:
>>> Hi all,
>>>
>>> Does anybody know whether it is possible to price a plain vanilla
>>> floating-to-floating cross-currency swap (e.g. EONIA vs Fed Funds)
>>> using quantlib. Does quantlib also possess functionality to build
>>> curves needed (one for EUR based on EONIA, one for USD based on Fed
>>> Funds Rate and cross-currency)?
>>>
>>> Many thanks in advance!
>>>
>>> Best regards,
>>> Kirill
>>>
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