On swap valuation and overnight rates

On swap valuation and overnight rates

In the past, deriving the market value of an interest rate swap was considered fairly easy. Nowadays, things have changed. Things which once seemed stable are now unstable and a risk-free rate is no longer without risk. For this reason, the valuation of any type of swap has to change. This article aims to throw some light on the major developments in the interest-rate derivatives markets, the emergence of a new methodology, and the underlying complexities in valuing diff erent kinds of swaps.

In the traditional method to value an interest-rate swap (IRS), a single curve is used both for estimating future cash fl ows (by using the forward rates implied from this curve) as well as for discounting them. Typically, this curve is the Euribor curve (for Euro swaps). The new methodology consists of using a diff erent discount curve to value swaps. The forward curve used in this methodology is also slightly diff erent – the bootstrapping of the forward curve needs to account for the new discount curve (this article won’t go into the details of this process).

Reasons to change

The key reasons behind the adoption of a new methodology are credit and liquidity premia and cash collateralization. During the crisis, it became apparent that having even the best-rated banks as counterparties is not actually risk free (e.g., a 3-month Euribor rate involves a 3-month credit exposure). Thus, cash collateralization and daily collateral calls became increasingly common for over-the-counter (OTC) derivatives. Because of daily mark-to-market and collateral calls, the relevant overnight rate is used to compute interest on the collateral. Therefore, for a cash-collateralized swap, the overnight rate (rather than the Euribor) denotes the opportunity cost of the collateral and is the correct starting point to value the swap. Common overnight rates are the Fed Funds Rate (for USD) and the Euro Overnight Indexed Average (EONIA, for Euro). Overnight Indexed Swaps (OIS) are interest-rate swaps where the fl oating leg is referenced against an overnight rate. With this background on OIS swaps, it is useful to observe the deviation between the OIS and Euribor swap rates. This deviation is an indicator of the additional credit and liquidity premia associated with the Euribor rate. As a particular example, it can be seen in the fi gure shown that as the credit crunch tightened, the spread between the 6M Euribor and 6M Eonia swap rates widened from nearzero levels to over 200 basis points in late-2008. An OIS curve can be constructed using OIS swaps of diff erent maturities. Extending the argument in the previous paragraph, the discount factors used for swap valuation should be derived from this OIS curve. So for an ordinary Euro swap, the Eonia curve should be used as the discount curve. In practice, the choice of discount curve should be determined by the applicable collateral agreements – thus depending on the type of collateral used to fund the swap, there can be diff erent discount curves.

Spread between 6M Eonia and 6M Euribor swap rates
Spread between 6M Eonia and 6M Euribor swap rates

OIS discounting and cross currency swaps

The principles discussed above apply to both single-currency as well as cross-currency interest-rate swaps (CCIRS). But crosscurrency swaps involve some additional complexities. To value a CCIRS, the forward curve is the same as for a regular IRS. So the Euribor curve or the Libor curve (depending on the leg currency) is used to estimate future cash fl ows. But the discounting is not straightforward – using just a discount curve is insuffi cient. The cross-currency basis spread must also be taken into account. These basis spreads between diff erent currencies exist because of demand/supply factors in global funding in diff erent currencies (e.g., many European banks have funding sources in EUR but commitments in USD), and the relative health of domestic banking systems (e.g., the EU banking system is currently vulnerable).

How to derive the OIS basis spread?

To account for the aforementioned cross-currency basis spreads, the discount curve of the foreign currency leg should be adjusted. E.g., for a Euro-USD swap, while discounting the foreign (USD) leg, the EUR-USD basis spread should be considered with the USD curve. But, as previously mentioned, most swaps are now cash collateralized and should be discounted using the OIS curve. The crux of the problem with valuing CCIRSs is that there is no liquid market (yet) for cross currency OIS basis swaps. The cross-currency basis swaps currently traded in the market are based on Libor (e.g. EUR-USD basis swaps trade the spread between the Euribor 3-month and USD Libor 3-month rates). It is theoretically wrong to add Libor basis-spreads to an overnight funding (OIS) curve. To get around this issue, some market participants try to derive the OIS basis spreads via Libor spreads. There is a liquid market to swap the Euribor against the Eonia, and the USD Libor against the USD OIS. It is also possible to swap the USD Libor against the Euribor. Thus three swaps can be set up in such a way that the Libor and Euribor legs are canceled out and the remainders are two OIS legs. The spread on this swap should be the crosscurrency OIS basis spread.

To clarify further, this illustration tries to derive the OIS basis spread between the USD (USD OIS) and the Euro (EONIA). An example trade1 incorporating the OIS cross-currency basis can be set up as:

Since there is no market yet for a direct trade like this, it can be broken down into three other trades:

From the above trades, the EUR-USD cross-currency OIS basis spread can be expressed as: [SpreadEONIA-USDOIS ≈ -SpreadUSD3M-USDOIS + SpreadUSD3M-EUR3M + SpreadEUR3M-EONIA]

While this approach represents a possible solution, it is yet to be seen if it would indeed hold once a market exists for OISbasis- swaps. The equation represents only an approximation based on certain assumptions and an accurate method can be 1 To keep matters simple, the required FX and convexity adjustments are not shown. developed only after the development of the cross-currency OISbasis- swap market.

Adoption in the market

The preceding paragraphs explain the need for OIS discounting, discuss its main concepts and challenges. It should be clarifi ed that although this article discusses OIS discounting in the context of swaps, the same discussion applies to collateralized (OTC) derivatives in general. In the swap market, some dealers had begun using OIS discounting to value their trades since 2008. In June 2010, LCH.Clearnet (the world’s largest swap clearing service) announced it would value all its swap portfolios using OIS discounting. Since October 2011, Bloomberg and Markit have offered the possibility to apply OIS discounting on swaps and other interest rate derivatives. Furthermore, some auditors now expect to see a company value swaps using the new methodology.


In conclusion, it is generally understood and agreed by market participants that OIS discounting is indeed the most appropriate method to value a swap. Considering that this is a relatively recent development, there are still some fi ner details to be ironed out. But with more counterparties applying the new methodology, and increasing support from leading software vendors, it can be expected that OIS discounting will soon be the new market standard.

A more detailed article on the fundamentals of cross currency swaps can be found here.