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Marco Bianchetti, a senior quantitative analyst in market risk management at Intesa Sanpaolo Bank, has a very intriguing piece out in this month’s Risk Magazine.
It’s highly technical, but the main point is that swap pricing has changed significantly since the beginning of the crisis, largely because the industry has found itself having to adopt a “double curve-single currency” framework.
The piece is entitled “Two curves, one price” and is based on this research paper, also by Bianchetti.
Essentially, as far as we understand, this all stems from the fact that single-curve no-arbitrage relations are no longer valid since inputs have become very different since the financial crisis kicked off.
So, despite the fact all the variables should arrive at one curve under the “no arbitrage” theory – they simply don’t any more, since many more factors have to be accounted for.
As Bianchetti states in his paper:
Numerical results show that the resulting forward basis curves may display a richer micro- term structure that may induce appreciable effects on the price of interest rate instruments.
And here’s an example in the shape of the EUR basis swap curve from February 2009, based on the four main Euribor contracts:
Before the crisis, Bianchetti says, the spreads would have been just a few basis points apart. As he notes:
Such evolution of the financial markets has triggered a general reflection about the methodology used to price and hedge interest rate derivatives, namely those financial instruments whose price depends on the present value of future interest rate-linked cash-fows.
Not only is the market charging wider spreads upfront in some cases, there is a clear adjustment going on for new practices, such as collateralisation and dealing with increased counterparty risk.
Previously, swaps on floating rate bonds would always be priced at par at the inception of the swap, as would Forward Rate Agreements — since FRAs could always be replicated in a similar fashion.
According to Fabio Mercurio, author of another paper on the topic, the relationship as it existed before was:
These consistencies between rates allowed the construction of a well-defined zero-coupon curve, typically using bootstrapping techniques in conjunction with interpolation methods…
Differences between similar rates were present in the market, but generally regarded as negligible. For instance, deposit rates and OIS (EONIA) rates for the same maturity would chase each other, but keeping a safety distance (the basis) of a few basis points. Similarly, swap rates with the same maturity, but based on different lengths for the underlying floating rates, would be quoted at a non-zero (but again negligible) spread.
But after August 2007, the variables began to diverge, and with that the structure of the different yield curves derived from the various contract types. Mercurio puts it like this:
The liquidity crisis widened the basis, so that market rates that were consistent with each other suddenly revealed a degree of incompatibility that worsened as time passed by. For instance, the forward rates implied by two consecutive deposits became different than the quoted FRA rates or the forward rates implied by OIS (EONIA) quotes.
Remarkably, this divergence in values does not create arbitrage opportunities when credit or liquidity issues are taken into account. As an example, a swap rate based on semiannual payments of the six-month LIBOR rate can be different (and higher) than the same-maturity swap rate based on quarterly payments of the three-month LIBOR rate.
So essentially, even though rates derived from today’s prices in similar durations and contracts began to diverge and plot totally different yield curves, these didn’t actually offer up arbitrage opportunities — or as it was once understood they should.
David at Deus Ex Macchiato summed up why this was the case back in June. As he noted, the market was probably accounting for Libor forward rates incorrectly from the beginning:
Standard theory says that you can derive 3m Libor 3m forward from 3m spot Libor and 6m Libor by saying that there is no free lunch "“ you should not be able to make money by borrowing for 3 m and then another 3 vs. lending for 6 or ther other way around.
Thus tenor swaps should price flat. But sadly 3m vs. 6m tenor swaps trade, and they do not price flat either. Ooops. So clearly the derivation of 3m Libor 3ms forward from a naive no arb argument is wrong. And that is how we have been deriving the Libor curve for 25 years. Big oops.
Hence, it is one thing to invest in Libor for three months and again for another three months — and quite another to invest on the offset for six.
As David noted:
…in a world where banks are risky, 3m then 3m is safer than investing for 6m thanks to the embedded credit option.
Meanwhile, the increased practice of collateralising swaps adds the complication of bolting the overnight index swapped rate into the equation too:
These days, again thanks to credit risk, most interdealer swaps trades are collateralised at least to some extent. And that collateral does not earn Libor, it earns OIS. Thus once think about replicating a swap's cashflows including collateral, you are naturally drawn to the OIS curve for discounting.
In short, it’s become incrementally more complicated to price such a thing as an interest rate swap.
Related links: In the land of two-tier rates – FT Alphaville "?General collateral remains puzzlingly inverted to fed funds' – FT Alphaville `Euribor has been vaporised – FT Alphaville
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