Identifying Equivalent EUR Swap Curves and Synthesizing OIS Basis
Summary
The document identifies Bloomberg’s EUR swap curve as the counterpart to its USD swap curve, explaining that both are built using comparable instrument sets and curve construction methods. The curves can be formed with or without OIS discounting. It points readers toward Bloomberg’s curve methodology documentation for details on instruments and bootstrapping choices.
It also shows how to combine cross-currency basis swaps with single-currency IBOR–OIS basis swaps to synthesize an OIS-based cross-currency basis. The worked example adds the quoted spreads from EUR/USD and the two currency-specific swaps. The resulting synthetic quote may differ slightly from a directly traded instrument because collateral terms can differ. The method can also be applied across IBOR tenors, with an additional basis swap needed to bridge tenors. The document offers an illustrative calculation rather than market data or a broader valuation framework.
Key ideas
- Bloomberg’s EUR swap curve is presented as the euro counterpart to its USD swap curve, using comparable construction methods.
- The curves may be built with or without OIS discounting.
- A cross-currency basis can be translated to an OIS basis by combining it with single-currency IBOR–OIS basis swaps.
- Collateral terms can create a difference between a synthetic basis and a directly traded instrument.
- The same synthesis can accommodate different IBOR tenors by including a tenor basis swap.
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Full text
# What is the EUR swap curve on Bloomberg? I.e. what is the EUR equivalent of S23 curve on Bloomberg? # What is the EUR swap curve on Bloomberg? I.e. what is the EUR equivalent of S23 curve on Bloomberg? I am trying to understand the currency basis calculation and whether there is a difference in currency basis when quoted vs. OIS and -IBOR rates. ## Answer by Olórin (score 3) https://quant.stackexchange.com/a/46261 The curve Bloomberg EUR swaps curve (YCSW0045 Index) is indeed the euro equivalent of the Bloomberg USD swaps curve (YCSW0023 Index). By equivalent I mean that each curves are constructed in the same manner : using sames types of instruments (deposits, FRAs, futures, swaps) with the same bootstrapping/implying method (exact fit vs best fit). For each you can also use OIS discounting or not. DOCS + "bootstrapping" or "curve" in the search field will bring you Bloomberg's "Building the Bloomberg Interest Rate Curve – Definitions and Methodology" pdf, as of march 2016, as far as I remember. This document is quite thorough (as thorough as could a Bloomberg technical document be ...) ## Answer by Attack68 (score 2) https://quant.stackexchange.com/a/35965 You can synthesise this with the single currency IBOR-OIS basis swap (SBS) in each currency. For example paying the EUR/USD 10Y XCS @ -40bps, represents paying 3M Euribor -40 versus receiving 3M USD Libor flat. If you then buy a EUR 10Y OIS/IBOR SBS @ 8bps, this represents receiving 3M Euribor -8bps and paying EONIA flat. If you then sell a USD 10Y OIS/IBOR SBS @ 20bps, this represents paying 3M USD Libor - 20bps and receiving FFOIS flat. Net you have synthesised paying a EUR/USD EONIA/FFOIS XCS @ -52bps (-40 +8 -20). Note: due to the credit support annex (CSA) on the EUR SBS being EUR cash collateral through any clearing house this is different to that on the specific XCS instrument which (if it traded) would be USD collateralised on all aspects of the trade, so this will have a minor (probably negligible) impact. Note: you can also use the same technique for other IBOR tenors such as 6M, where the standard XCS is 3M IBOR and there is a 3M/6M SBS market in each currency.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.