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MikeJuniperhill
Topic Author
Posts: 57
Joined: February 7th, 2004, 11:57 am

### Solving XCCY basis spread by using IR-FX parity

I am currently working on the task for finding out, how to calculate XCCY basis spreads for short-end of the corresponding curve. I have a strong hypothesis, that this could be possible by using a bit modified version of standard FX-IR parity. Below are my thoughts. Assume currency pair EUR/USD

"Standard" parity formula:
(1 + R_eur * dt) = (FX_spot / FX_forward) * (1 + R_usd * dt)

where:
R_eur = EUR deposit rate for a given tenor
R_usd = USD deposit rate for a given tenor
dt = tenor length in years

"Modified" parity formula:
(1 + [R_eur + S] * dt) = (FX_spot / FX_forward) * (1 + R_usd * dt)
where S is XCCY basis spread. This spread can then be solved:
S = (((FX_spot / FX_forward) * (1 + R_usd * dt) - 1) * (1 / dt)) - R_eur

Assume the following data (ICE dataset as of 1.11.2018):
FX spot=1.1388
FX forward points for 3M=0.009713
EUR deposit rate for 3M=-0.00318
USD deposit rate for 3M=0.025815

By using that "Modified" parity formula and solving basis spread for 6M, I will get -24.622 bps, which is pretty close to Bloomberg closing mid quote of -25.048 for the same day. Also, we need to take into account, that Bloomberg spread is an actual quoted spread, while my spread is theoretical, so (AFAIK) those two should not even be the same exactly.

Any clever opinions on this? If you have tackled with the same issue, what was your solution?

MikeJuniperhill
Topic Author
Posts: 57
Joined: February 7th, 2004, 11:57 am

### Re: Solving XCCY basis spread by using IR-FX parity

Sorry, a small correction. Should have been:

By using that "Modified" parity formula and solving basis spread for 3M, I will get -50.514 bps, which is quite close to Bloomberg closing mid quote. dt = 0.25

I have noticed the following issues:
• modified parity holds quite well for liquid major currencies, but it is less accurate for "less important" currencies (INR, TRY, etc.). I suspect this might actually be data-related issue.
• results are "more off" for shorter the maturities (6M is more close to real quotes than 3M or 1M calculated spreads, and so on)
Regards, Mike Juniperhill

MikeJuniperhill
Topic Author
Posts: 57
Joined: February 7th, 2004, 11:57 am

### Re: Solving XCCY basis spread by using IR-FX parity

Some thoughts here. Have a great weekend.
-Mike

Randor
Posts: 54
Joined: October 8th, 2005, 8:33 am

### Re: Solving XCCY basis spread by using IR-FX parity

looks good to me
most currencies aside from some majors do not have quotes on the 3m xccy basis
so for them, bbg may be implying them from the fx market as per your formula

also note that the implied xccy basis spread will depend on your collateralisation

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