Cross currency basics 2 - Pricing and convexity
On 5 January 2022 I posted a blog looking at some basic features of cross-currency swaps. I included quote conventions, term structure, positive/negative spreads, convexity, calculating margins and XVAs. This was a lot to cover in a single article, but these are important building blocks for a better understanding of this important product.
This time I will look more at some practical examples of how to price some swaps. I will not go into great depth on the actual pricing process, but I will find a few examples to demonstrate the convexity and crosses. I will also cover the differences between IBOR (including LIBOR) and RFR (Risk Free Rates) pricing; a topical subject at the moment.
The RFR-based cross-currency swap markets are developing quickly so we need to be very aware of how this affects the pricing. The Clarus posts from December 2021 for the new, RFR-based swaps were also covered by Risk in January 2022 and they both really show how RFRs are replacing LIBOR (and other IBORs) in many markets. You can still access LIBORs, but they will be using fallbacks (usually to ISDA) after a cessation or pre-cessation event.
This mix-and-match approach is making it difficult for many firms to accurately price cross-currency swaps. Pricing inputs are changing, and revaluation curves need to be kept up to date. System compatibility issues are a constant concern as we move to new pricing input conventions.
Convexity and pricing
Let us take a simple example to see the impact of convexity on the pricing for a 5-year AUD/USD cross-currency swap. We will use the current convention of SOFR/BBSW for this example. All the spreads are in basis points.
USD/AUD (RFR/IBOR)
Base curve USD SOFR flat / AUD BBSW (3-month) + 4
Now we add 100 bps to the USD SOFR rate to match an actual cashflow from, for example, a debt issue.
Trade rate USD SOFR + 100 / AUD BBSW (3-month) + 106.5
The AUD spread is 106.5 bps which is higher than the simple estimate of 4 + 100 = 104 bps.
This is convexity in practice. The 5-year SOFR rate is 1.40% and the 5-year AUD BBSW rate is 1.76%. The additional 0.36% (1.76 – 1.40) makes a difference of 2.5 bps over the 5 years. The higher rate for AUD (and therefore a higher discounting rate) than that of USD leads to this outcome.
But just one technical note, remember the SOFR and BBSW are different basis, respectively 360 and 365 days which must also respected.
EUR/USD (RFR/RFR)
Next example: EUR/USD cross currency.
Base curve USD SOFR flat / EUR €STR - 18
Now we add 100 bps to the USD SOFR rate to match an actual cashflow, say from a debt issue.
Trade rate USD SOFR + 100 / EUR €STR + 77.8
The EUR spread is 77.8 bps which is 4.2 bps lower than the simple estimate of -18 + 100 = 82 bps.
The 5-year SOFR rate is 1.40% and the 5-year €STR rate is -.05%. The additional 1.45% (1.40 + 0.05) makes a difference of -4.2 bps over the 5 years. This time, the convexity adjustment is negative because EUR rates are lower than USD rates.
JPY/AUD (RFR/IBOR)
Finally, something a little more radical; JPY/AUD cross currency. We will stay with the theme and use TONA/BBSW for the floating rates.
Base curve JPY TONA flat / AUD BBSW (3-month) + 58
Now we add 100 bps to the USD SOFR rate to match an actual cashflow, say from a debt issue.
Trade rate JPY TONA + 100 / AUD BBSW (3-month) + 164.75
The AUD spread is 164.75 bps or 6.75 bps higher than the estimate of 58 + 100 = 158 bps.
The 5-year TONA rate is 0.04% and the 5-year AUD BBSW rate is 1.76%. The additional 1.72% (1.76 - 0.04) makes a difference of 6.75 bps over the 5 years.
The message in all of this is clear; the calculations need to be done properly and with great care, otherwise, your pricing may be significantly different to the correct outcome.
The cross-currency debate: is the EUR leg adopting €STR or Euribor as the convention?
At the time of this blog, the EUR/USD cross-currency swaps are being routinely quoted in the interdealer markets as €STR/SOFR even though Euribor is still published. There are many reasons why this is the case including the (generally) lower volatility of the RFR/RFR spreads when compared with RFR/IBOR. I will return to the volatility question in a future blog, but the fact remains, €STR/SOFR seems to dominate.
As above, the EUR/USD cross currency swap is quoted (€STR/SOFR) as:
Base curve USD SOFR flat / EUR €STR - 18
The basis swaps are:
SOFR/Euribor USD SOFR flat / EUR Euribor - 31.25
LIBOR/Euribor USD SOFR flat / EUR Euribor - 9.5
The math is straight forward and there are some convexity differences as well.
EUR Euribor / €STR + 13.25 -> USD SOFR flat / EUR €STR – 31.25 (- 18 - 13.25)
USD LIBOR / SOFR + 22.9 -> USD SOFR flat / EUR Euribor – 8.35 (- 31.25 + 22.9)
Our simple calculation shows the approximation of - 8.35 is similar to the market rate of - 9.5. However, it is not exact, and we can again see the impact of convexity.
Pricing properly is the key. Approximations are a great idea to check to price, but a full calculation is always the best approach.
Mix-and-match
As I described in the previous blog, conventions vary across currencies. While the LIBOR currencies and EUR have moved convincingly to the RFR/RFR convention, others are at different stages and are using various conventions.
Local preferences can be important (e.g., AUD) where the RFR/IBORs persist. However, this may change as inter-dealer markets eventually settle on conventions where markets are most liquid.
The best approach is to be very clear about your pricing inputs:
What is the basis? RFR/RFR or something else?
How is your pricing process geared to deal with different inputs and basis?
Is your revaluation system and process correctly using new curves?
As the cross-currency markets evolve and change, many firms will have challenges keeping abreast of the issues and will need to adjust their processes accordingly.
Summary
Many buy-side firms use cross-currency swaps to hedge assets and/or liabilities in non-domestic markets. This often results in large basis point spreads in the offshore currency which are then converted to the home currency plus/minus a spread. It is the combination of large spreads and different discounting rates that can create the convexity problem.
It is good practice to perform the simple calculation to get a ‘ballpark’ estimate of the likely outcome of a pricing calculation. While this help establish the approximate spread, the full and correct calculation must be performed to check pricing.
Cross-currency markets are changing, and the quoted price may not always be the one you have been using previously. A mix of RFR/RFR, RFR/IBOR and IBOR/IBOR conventions are all in the markets now. Proper alignment of the pricing and revaluation systems is essential and often quite complex. Incorrect inputs and calculations can cause issues with deal pricing and agreeing collateral amounts if not managed carefully.
As always, Martialis has significant expertise in pricing derivatives including cross-currency swaps. Let us know if you need some assistance or just want to check a few points.