How Cross-Currency Swaps Relate to Interest Rate Swaps

# Cross currency swap a combination of 2 Interest rate swap


# Cross currency swap a combination of 2 Interest rate swap












I was told that a Cross currency swap can be thought of as a portfolio of 2 different interest rate swaps.

Reference link : https://cvacentral.com/wp-content/uploads/2020/06/Chapter-11-Appendices-4E.pdf (page 4)

Can you please help me to understand intuitively how this is the case? Typically, in Interest rate swap, we have fixed leg and floating leg in same currency. In Cross current swaps cash flows the exchanged in different currencies. So, how exactly one can define fixed legs for cross currency swap?

## Answer by AKdemy (score 2, accepted)

https://quant.stackexchange.com/a/74024

You missed to mention a lot of details in your link.

- Firstly, the XCCY Swap is said to be an approximation of an FX forward and swaps, not just swaps.

- Secondly, the FX swap is approximated.

- Thirdly, the swaps are approximated, assuming a flat yield curve (which is never the case).

- It is for approximating potential future exposure (PFE), not the CCY swap itself.

Long story short: As @Dimitri Vulis explained, this statement does not generally hold, and is at best an approximation. However, this Citibank webpage illustrates how you can decompose fixed to fixed (FXFX) and fixed to float (FXFL) cross currency swaps into swaps (and basis swaps). If you substitute the basis swap for the FX forward, you have the decomposition used in your paper.

Short story long: Generally, all sorts of cross currency swaps exist (FXFX, FXFL and FLFL), but the market mainly quotes spreads on cross currency FLFL swaps that are mark-to-market (MTM), also known as cross currency basis swaps. The market quote is a spread on top of the foreign leg which makes the present value of float leg in the foreign currency equal to present value of float leg in USD currency. Based on the date your reference was written, I assume most XCCY swaps were still in Libor / Euribor and not RFR (ESTR / SOFR).

In a perfect no arbitrage world the following would hold: If you life in Europe, but have a firm in the US with funding needs, you can take a loan from your local bank. However, there is a mismatch between the loan payments in EUR, and your costs in USD. To hedge this FX risk, you can enter a XCCY swap, which allows you to swap EUR into USD at today's FX rate, with the agreement to simply swap back at the end at the same rate, eliminating FX risk. Since the USD aren't owned by you (they are effectively borrowed), you need to pay back USD interest (LIBOR) and will receive EUR (Euribor) interest form your counterparty. That would be it.

In reality, markets aren't perfect and there are demand and supply factors to consider (as well as credit risk...). Generally, there is higher demand for USD (many transactions are based or financed in USD). Therefore, the counterpart paying Euribor will need to be compensated for lending the USD. This is why there is a basis spread, as shown in the Bloomberg screenshot below.

You can also see that it is MTM and that you adjust your principal every period. The initial notional in EUR is computed based on the FX rate, and the FX rate displayed in the Cashflow table on the right is the inverse quote (USDEUR). The valuation at initiation uses FX forwards (can be quoted or computed using covered interest rate parity) for future FX rates.

Based on your example with using FX forwards, you implicitely have the cross currency basis in your approximation, because you can use Fwd FX rates to calculate the implied borrowing cost in another currency. For example, the implied basis can be derived from Covered Interest Rate Parity from making a 3 month EURIBOR loan and converting it into USD via a 3 month FX swap. The difference between the implied cost and the 3m Libor curve is the basis.

There is a special case where the approximation in the reference works better for XCCY swaps that are mark-to-market (MTM): Without dual curve stripping (it is market pratice to discount using OIS / RFR), there will be no pricing difference between MtM and non-MtM basis swaps. In Bloomberg jargon, if you disable OIS discounting/DC stripping in SWPM it will strip S92 assuming 3m$\\\$$LIBOR as the interest rate on collateral and the MTM resets will therefore have no pricing difference to non-MTM version, by definition of 3m$\\\$$L discounting and 3m$\\\$$L floating leg.

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/74014

I can think right away of a few features that some cross-currency swaps have that a setup for pricing and risk-managing single-currency interest rate swaps may not be able to handle correctly:

- in a float v float cross-currency swaps, the notional usually changes with time (resets).

- the pricer needs to know how to use a cross-currency basis. The risk calculator needs to calculate the sensitivities to it.

- swaps for some currencies are usually non-delivery. The pricer needs to know to observe some official exchange rate a few days before a cash flow and to use that, rather than live, rate after it is frozen.

There may be other features I don't recall right now.

But a typical, physical delivery, fix v fix or fix v float, cross-currency swap can be viewed as a combination of two interest rate swap legs. Unlike IR swaps, you must include principal exchange.

While a typical interest rate swap is fixed v float (same currency), people trade basis swaps (e.g. 3mo libor v 6mo libor; sofr v fed funds), and various inflation-linked legs (not quite the same as float legs because both the interest and the principal are inflation-adjusted). These work with cross-currency swaps as well. E.g. inflation-linked fixed Chilean peso versus floating USD is surprisingly liquid.

## Answer by Randor (score 1)

https://quant.stackexchange.com/a/74015

"I was told that a Cross currency swap can be thought of as a portfolio of 2 different interest rate swaps."

Indeed , a cross currency swap can have it's interest rate risk from each of the currencies hedged by trading an interest rate swap in that currency<*>.

However, the coss-currency basis risk would still remain.

Note that I have described how to hedge , not how to synthesize to match the price. In fact , that should be do-able, do the other leg versus OIS so it's value is par... Maybe for one of the legs there will be a bit of a problem because you'll need your CSA in a different currency...

<*> 2nd leg of the swap would be OIS.