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BerndSchmitz
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Posts: 232
Joined: August 16th, 2011, 9:48 am

Why are EUR/USD, GBP/USD and EUR/GBP Cross-Currency-Spreads so perfectly in line?

May 19th, 2017, 8:35 am

Hi,

I just used the EUR/USD and GBP/USD CCY-Spreads (quoted on Bloomberg) to calculate synthetic EUR/GBP CCY-Spreads. I then compared those to the quoted EUR/GBP CCY-Spreads. The mids are always in line up to 0.125 bp:
       quoted EUR/GBP    synthetic EUR/GBP
1Y        17.500                     17.375
2Y        18.750                     18.750
3Y        20.750                     20.750
4Y        22.500                     22.500
5Y        24.750                     24.625
7Y        27.250                     27.125
10Y      28.750                     28.750
15Y      22.500                     22.375
20Y      16.000                     16.000
30Y      13.500                     13.500

To be honest I did not expect that because the synthetic EUR/USD CCY-Spread is in fact not the same as the quoted one for 2 reasons:
- EUR/USD and GBP/USD CCY Swaps both reset on the USD leg. If you pay the USD leg in one swap and receive it in the other you end up with a constant notional (!) EUR/GBP CCY Swap. Shouldn't in general resettable and constant-notional CCY Spreads be different?
- EUR/USD and GBP/USD CCY Swaps are typically USD collateralized and so is the synthetic EUR/GBP CCY Swap. However, the quoted GBP/EUR CCY Spreads are EUR collateralized, aren't they? I thought that nowadays the market quotes different CCY Spreads depending on the collateralization

What is your opinion on that?

Thanks,
Bernd
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EUR_USD_CCYSpreads.png
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Martinghoul
Posts: 3214
Joined: July 18th, 2006, 5:49 am

Re: Why are EUR/USD, GBP/USD and EUR/GBP Cross-Currency-Spreads so perfectly in line?

May 21st, 2017, 8:59 am

Have you tried to quantify how much the differences you mention are worth, in basis points?
 
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antoineconze
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Joined: September 21st, 2015, 2:01 pm

Re: Why are EUR/USD, GBP/USD and EUR/GBP Cross-Currency-Spreads so perfectly in line?

May 22nd, 2017, 9:24 am

Actually if you compute the synthetic spread as the difference between the spreads of a EURUSD XCCY and a GBPUSD XCYY you end up with a constant notional EURGBP that pays a spread on each leg, rather than the synthetic spread on one leg and no spread on the other leg, so that's not even a standard constant notional EURGBP XCCY.  
 
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BerndSchmitz
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Posts: 232
Joined: August 16th, 2011, 9:48 am

Re: Why are EUR/USD, GBP/USD and EUR/GBP Cross-Currency-Spreads so perfectly in line?

May 24th, 2017, 7:51 am

 @antoineconze: Thanks for pointing that out. However, what I can do is simply put all spreads on one leg. I only have to account for the different daycount-conventions of the EUR leg (Act/360) and the GBP leg (Act/365)
@Martinghoul: No, I have not yet done it. At one point I will definitely do this for the constant notional vs. resetting. However, I think it's not possible to do this for the collateralization issue. According to my traders this can produce a difference of up to 0.75bp. However, admittedly this is for a different currency pair
 
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antoineconze
Posts: 2
Joined: September 21st, 2015, 2:01 pm

Re: Why are EUR/USD, GBP/USD and EUR/GBP Cross-Currency-Spreads so perfectly in line?

May 24th, 2017, 8:46 am

 @BerndSchmitz: you cannot simply move a spread from one leg to the other, because even if the day count conventions were the same on both legs, the PV01s would be different, as each leg is discounted by its own discount curve, each discount curve being the synthetic funding curve built from the collateral currency curve and the leg currency/collateral currency forward FX.  For instance a constant notional XCCY Libor USD flat vs Euribor - 20 bps and a constant notional XCCY Libor USD + 20 bps vs Euribor flat, both USD collateralized, do not have the same PV.

To do an exact comparison between the quoted EURGBP and the synthetic EURGBP XCCY I think you first have to bootstrap the EURUSD FX forwards and the GBPUSD FX forwards, then obtain the synthetic EURGBP forwards as the ratio of the formers, and finally from that synthetic curve reprice the EURGBP XCCY to find the spread that makes its PV = 0.

To do an approximate comparison you can do this:
  •  start with the case of 1 period (3 months) XCCY swaplets that start today. If you disregard the difference in discount factors between 3 months EUR discounting and 3 month GBP discounting then you will see that the 1 period EURGBP spread should be equal to approximately the difference between the 1 period GBPUSD spread and the 1 period EURUSD spread (there would be no approximation if the spreads were paid upfront, the day count applied to the spreads were all  the same, and the EURGBP swaplet was collateralized in USD)
  • next consider that a resettable XCCY is just a sum of forward start 1 period XCYY swaplets, and you obtain that the resettable EURGBP XCCY spread is approximately equal to the difference between the resettable GBPUSD spread and the resettable EURUSD spread.
I think that explains why your "synthetic" and your actual EURGBP quotes are very close.
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