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Topic Title: Boostrapping a Yield Curve Using FX Forward Points
Created On Tue Oct 19, 10 10:43 AM
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thusi
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Tue Oct 19, 10 10:43 AM
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Hi,

Hi,

I want to build an implied YC using CADUSD FX Forward Points. I have the following FX Fwd Point Information.

ON
TN
1d
2d
1W
2W
...
3M
6M
9M
1Y
2Y
3Y
..
10Y

I can use the FX arbitrage to get the short end of the curve. That is 1d, 2d ... 3M, 6M, 9M, 1Y rates assuming the USD yield curve.
That is, we know Spot rate, Forward Rate and US interest rate, from that we can find out CAD Interest rate.

The one I am not that clear on is how to calculate the swap rates for 2Y, 3Y ...

Could some one explain how this can be done.


Thanks

-------------------------
thusi

Edited: Tue Oct 19, 10 at 10:19 PM by thusi
 
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thusi
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Tue Oct 19, 10 10:13 PM
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I am bit surprise that no one has answered the question. Is it because no one builds Yield Curves using the implied rates of FX quotes?


-------------------------
thusi
 
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Martinghoul
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Wed Oct 20, 10 11:24 AM
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I think you may find that there's a couple of very helpful bits by cpulman on the subject...

-------------------------
"Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
 
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vdiclemente
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Wed Oct 20, 10 01:51 PM
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Hi Thusi,

You dont build the Yield curve using FX Forward. The FX Forward should be an output of you both yield curve (ccy1 and ccy2). In order to match you FX Forward you need to incoporate in your stripping the cross currency swap points. So you boostrap using Depo (below 1y), Swap (after 1y), Basis Swap and on top of that at cross ccy swap.

Good luck
 
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daveangel
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Wed Oct 20, 10 02:08 PM
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Quote

Originally posted by: vdiclemente
Hi Thusi,

You dont build the Yield curve using FX Forward. The FX Forward should be an output of you both yield curve (ccy1 and ccy2). In order to match you FX Forward you need to incoporate in your stripping the cross currency swap points. So you boostrap using Depo (below 1y), Swap (after 1y), Basis Swap and on top of that at cross ccy swap.

Good luck


not true at all. think of a market where you dont have access to depos and thnk about how you fund a position in such a market.

-------------------------
Knowledge comes, but wisdom lingers.
 
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vdiclemente
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Wed Oct 20, 10 02:14 PM
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Well you are right! I was thinking specially in G10. For the NDF market you boostrap directly out of NDF, my apologize! I didnt want to be general but try to guess the root of the original question
 
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thusi
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Wed Oct 20, 10 10:22 PM
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Thanks all for the replies.

The short end of the curve can be calculated easily as the Fx forward points are available since the markets are liquid. But for the long end; only 2Y, 3Y, 4Y ... 10Y data are available. One way of calculating this is to first calculate the implied fx forward rates for missing points such as 2Y3M, 2Y6M, 2Y9M, 3Y6M, ... etc. After these, we can calculate the implied zero rates and then use this to calculate the implied swap rate.

From this we can calculate the implied Yield Curve from Fx Forward Points (Fx Forward rates). That is the method I am using right now.

Thanks Martingoul, I will have a look at what cpulman has written. Has he published any papers? Couldn't find his name in google. I found the following document by him on Wilmott.
Consistent Pricing of FX Forwards, Cross-Currency Basis Swaps, and Interest Rate



-------------------------
thusi

Edited: Wed Oct 20, 10 at 10:23 PM by thusi
 
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vdiclemente
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Thu Oct 21, 10 09:20 AM
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Sorry Thusi, but I disagree what you are doing? What ccy are you building the yield curve fro? For G10, EUR, USD, JPY, CHF, etc... you way it is not the way... If you want to build a yield curve consistent up to 10y and match the FX Forward Rate you have to boostrap from depo, Swap, Basis Swap and Cross Currency Swap, dont use Future because of the nature of the instrument.... For ccy (BRL, RUB, etc) where you dont have Swap market liquid enough at long dated you can build out of NDF (non-deliverable forward) - dont use onshores!, but you can get up to 2y most of the cases but who cares since there is not market beyond that...
 
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cpulman
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Mon Oct 25, 10 11:47 AM
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Hi,

If you are building a discount curve for pricing FX Forwards, while I agree you should definitely be using futures/swaps/basis swaps for >1yr, for 1yr and below you should be using the fx forwards themselves as they are far more liquid than the deposit & xccy basis swap market sub-1yr. You can then "imply" xccy basis spreads for sub-1y (if you stick the deposits into your curve), but these are purely arbitrary (as is sticking in USD deposits for your US curve) given that you will probably not be able to trade the deposit market.
 
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pimpel
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Tue Oct 26, 10 09:23 AM
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Quote

Originally posted by: cpulman
Hi,

If you are building a discount curve for pricing FX Forwards, while I agree you should definitely be using futures/swaps/basis swaps for >1yr, for 1yr and below you should be using the fx forwards themselves as they are far more liquid than the deposit & xccy basis swap market sub-1yr. You can then "imply" xccy basis spreads for sub-1y (if you stick the deposits into your curve), but these are purely arbitrary (as is sticking in USD deposits for your US curve) given that you will probably not be able to trade the deposit market.


You can ommit such problem, by assuming, that you can borrow/lend at ON, so you change longer term deposits with OIS swaps and you are at home.
 
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cpulman
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Tue Oct 26, 10 03:10 PM
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Well, yeah it's a big improvement, but it's still purely arbitrary. I can remember plenty of times when I wasn't able to fund my fwd book at OIS, for example, as it's a fixing rather where you actually fund your book. There's still a cross-currency basis issue between two currencies' OIS because OIS represents an uncollateralised overnight rate and the o/n fx swap is essentially collateralised by the foreign currency (or dollars, depending on which way you are around) and also has the embedded fx optionaility on jump to default. There is an EONIA/FedFunds basis swap market, which currently has the 1yr basis swap at -19.75bps, so you should get an idea of just how much you will be out building a curve for pricing FX Forwards using just OIS.
 
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Ziggy
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Tue Oct 26, 10 09:45 PM
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I was planning to write something here about the difference between "libor curves" and "risk-free" curves in calibration. However, Piterbarg/Andersen (*) have much better presentation than anything I could have written, so make sure you check out chapter 6.5 in the first volume [Various Topics in Discount Curve Construction]

From practical experience I can testify that using the local interbank curves (depos plus IRS) as a proxy for domestic risk-free discount rates can turn out to be a very dangerous exercise. This proved to be the case two years back when the difference between interbank rates and "FX based risk-free rates" soared to 6-8% in a small Scandinavian country with an active FX market and free capital flow at the time.

(*) Received my set early today and am very impressed.
 
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vdiclemente
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Wed Oct 27, 10 09:37 AM
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Ziggy, did you check at that time how much was the cross ccy swap? Without the cross ccy swap you will never match the FX forward using just depo and IRS
 
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pimpel
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Wed Oct 27, 10 12:44 PM
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Quote

Originally posted by: Ziggy
I was planning to write something here about the difference between "libor curves" and "risk-free" curves in calibration. However, Piterbarg/Andersen (*) have much better presentation than anything I could have written, so make sure you check out chapter 6.5 in the first volume [Various Topics in Discount Curve Construction]

From practical experience I can testify that using the local interbank curves (depos plus IRS) as a proxy for domestic risk-free discount rates can turn out to be a very dangerous exercise. This proved to be the case two years back when the difference between interbank rates and "FX based risk-free rates" soared to 6-8% in a small Scandinavian country with an active FX market and free capital flow at the time.

(*) Received my set early today and am very impressed.


It is good, though I think that the paper below is much better on the subject:

http://ssrn.com/abstract=1440633

Actually Andersen and Piterbarg cite this as reference, but they missed one point actually solved in the paper.
 
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Ziggy
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Wed Oct 27, 10 02:12 PM
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Pimpel: Followed the reference and read the paper yesterday. I have to say I completely agree with you

vdiclemente:
" Ziggy, did you check at that time how much was the cross ccy swap? Without the cross ccy swap you will never match the FX forward using just depo and IRS"
Actually the case I was referring to had only active FX forward, long-term FX swaps were at this point long-gone. Still allows us to have two separate curves for the one year, index curve and discount curve.
 
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pimpel
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Wed Oct 27, 10 02:53 PM
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Originally posted by: Ziggy
Pimpel: Followed the reference and read the paper yesterday. I have to say I completely agree with you



Did you find the other reference on the subject by Traven?
 
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Ziggy
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Fri Oct 29, 10 04:38 PM
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Quote

Originally posted by: pimpel

Did you find the other reference on the subject by Traven?


No didn't find it. Would be very interested to give it a quick read if anyone has it.

I am very happy with the papers by Fujii et. al. Results are mostly in line with my practical experience, although I do have a list of comments.
 
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