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Correct way to price fx forward

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Boris Chow

Correct way to price fx forward

Hi all,

I would like to ask if there is any standard way to price fx forward.

In my old company, I see they use the yield curve to discount the forward curr1 and curr2 , and use current spot rate of report currency against them to do the final NPV.

But I also hear that some others use current spot rate + forward point of curr1/curr2 to calculate the difference between new curr2 and original curr2.

What is the more popular way?

Thanks a lot,
Boris
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Peter Caspers-4

Re: Correct way to price fx forward

Hello Boris,

usually one bootstraps fx curves using a reference OIS curve
consistent with the CSA currency of the market's fx forward quotes
(given as points over spot as you already mentioned). Then for pricing
of a collaterized fx forward you have to translate these curves to
your deal CSA currency, which defines a new OIS reference curve. This
can for example be done by assuming constant fx forwards when moving
to the new reference curve.

Does that help ?

Best regards
Peter

On 18 August 2015 at 16:11, Boris Chow <[hidden email]> wrote:

> Hi all,
>
> I would like to ask if there is any standard way to price fx forward.
>
> In my old company, I see they use the yield curve to discount the forward curr1 and curr2 , and use current spot rate of report currency against them to do the final NPV.
>
> But I also hear that some others use current spot rate + forward point of curr1/curr2 to calculate the difference between new curr2 and original curr2.
>
> What is the more popular way?
>
> Thanks a lot,
> Boris
> ------------------------------------------------------------------------------
> _______________________________________________
> QuantLib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users

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Boris Chow

Re: Correct way to price fx forward

Thanks a lot Peter.

If we have a forward contract of EURJPY, (buy EUR at future) , do we need both OIS curves of both JPY n EUR? Are the OIS curves built upon par swap rate where floater is using OIS, or it is an implied curve of cross currency using forward point?

If the market is not liquid enough, what should we use for long tenor?

Please advise what is CSA currency and is it base / quoted or reporting currency?

Thanks a lot,
Boris

> On 19 Aug, 2015, at 1:40 am, Peter Caspers <[hidden email]> wrote:
>
> Hello Boris,
>
> usually one bootstraps fx curves using a reference OIS curve
> consistent with the CSA currency of the market's fx forward quotes
> (given as points over spot as you already mentioned). Then for pricing
> of a collaterized fx forward you have to translate these curves to
> your deal CSA currency, which defines a new OIS reference curve. This
> can for example be done by assuming constant fx forwards when moving
> to the new reference curve.
>
> Does that help ?
>
> Best regards
> Peter
>
>
>> On 18 August 2015 at 16:11, Boris Chow <[hidden email]> wrote:
>> Hi all,
>>
>> I would like to ask if there is any standard way to price fx forward.
>>
>> In my old company, I see they use the yield curve to discount the forward curr1 and curr2 , and use current spot rate of report currency against them to do the final NPV.
>>
>> But I also hear that some others use current spot rate + forward point of curr1/curr2 to calculate the difference between new curr2 and original curr2.
>>
>> What is the more popular way?
>>
>> Thanks a lot,
>> Boris
>> ------------------------------------------------------------------------------
>> _______________________________________________
>> QuantLib-users mailing list
>> [hidden email]
>> https://lists.sourceforge.net/lists/listinfo/quantlib-users

Peter Caspers-4

Re: Correct way to price fx forward

Hi Boris,

here is my view on this; assuming you have fx swap point market quotes
EUR-USD and JPY-USD with implicit CSA currency USD (i.e. the quotes
refer to instruments collaterized in USD, this needs to be checked in
each individual case) you would build two curves

EUR-USD FX
JPY-USD FX

against the USD OIS (FedFund) curve. The USD OIS curve itself is built
using e.g. USD FedFund swap quotes in the usual, single currency way.
The two FX curves on the other hand are implied from the fx point
quotes only, not using any single currency instruments in EUR or JPY.
In this sense they are kind of "artificial" curves with the only
purpose of replicating the fx forward quotes (together with the USD
FedFund curve).

Next step would then be the translation to your deal CSA currency.
Assuming e.g. EUR as the collateral currency of your deal (and
provided your deal is collaterized in the first place, otherwise the
situation is different ... is it ? ..., and the interest paid /
received on the collateral is the EONIA ON fixing flat) you build a
new curve

JPY-EONIA FX

against the EUR OIS curve (again built from the usual single currency
EONIA swap quotes). You have some freedom how to do this, but a common
way would be to require that the implied JPY-EUR FX forwards are equal
to those implied from your two initial curves EUR-USD FX and JPY-USD
FX.

You can then discount the JPY amount on JPY-EONIA FX, convert it with
the current spot (applicable to your valuation date which might need
another, smaller adjustment of the spot quote, if the value date of
the latter is not equal to the valuation date) and the EUR amount on
EONIA. This is your EUR fair value of the fx swap.

Conversion of the EUR npv to the reporting currency if different from
EUR would not involve any specialities compared to other instruments
valued natively in EUR (say a plain vanilla EUR swap) in my opinion.
But maybe I am missing something in this part of your question.

Thank you
Peter

On 19 August 2015 at 03:03, Boris Chow <[hidden email]> wrote:

> Thanks a lot Peter.
>
> If we have a forward contract of EURJPY, (buy EUR at future) , do we need both OIS curves of both JPY n EUR? Are the OIS curves built upon par swap rate where floater is using OIS, or it is an implied curve of cross currency using forward point?
>
> If the market is not liquid enough, what should we use for long tenor?
>
> Please advise what is CSA currency and is it base / quoted or reporting currency?
>
> Thanks a lot,
> Boris
>
>> On 19 Aug, 2015, at 1:40 am, Peter Caspers <[hidden email]> wrote:
>>
>> Hello Boris,
>>
>> usually one bootstraps fx curves using a reference OIS curve
>> consistent with the CSA currency of the market's fx forward quotes
>> (given as points over spot as you already mentioned). Then for pricing
>> of a collaterized fx forward you have to translate these curves to
>> your deal CSA currency, which defines a new OIS reference curve. This
>> can for example be done by assuming constant fx forwards when moving
>> to the new reference curve.
>>
>> Does that help ?
>>
>> Best regards
>> Peter
>>
>>
>>> On 18 August 2015 at 16:11, Boris Chow <[hidden email]> wrote:
>>> Hi all,
>>>
>>> I would like to ask if there is any standard way to price fx forward.
>>>
>>> In my old company, I see they use the yield curve to discount the forward curr1 and curr2 , and use current spot rate of report currency against them to do the final NPV.
>>>
>>> But I also hear that some others use current spot rate + forward point of curr1/curr2 to calculate the difference between new curr2 and original curr2.
>>>
>>> What is the more popular way?
>>>
>>> Thanks a lot,
>>> Boris
>>> ------------------------------------------------------------------------------
>>> _______________________________________________
>>> QuantLib-users mailing list
>>> [hidden email]
>>> https://lists.sourceforge.net/lists/listinfo/quantlib-users