Podcast: Georgios Skoufis on RFRs, convexity adjustments and the Sabr model

Interest payments linked to risk-free rates (RFR) are typically calculated by compounding the string of overnight fixings over a given period. This is the norm for transactions between financial counterparties. Corporate clients, however, often find it more intuitive to use an arithmetic average of overnight rates. While this makes life easier for clients, it leaves dealers with a tricky problem to solve.

The arithmetic average and compounded rate can diverge over time. At times, the difference can be greater than the bid-offer spread. So, dealers must calculate a convexity adjustment to keep the rates aligned and avoid being arbitraged.  

“The convexity adjustment for a 30-year average rate RFR swap with the market standard one-year frequency is roughly around -2 basis points,” says Giorgios Skoufis, cross-asset quant analyst at Bloomberg, while the bid-ask spread is normally around half a basis point. 

In this episode of Quantcast, Skoufis explains how this convexity adjustment can be calculated more efficiently for interest rate swaps that reference RFRs.

Dealers typically use one of two standard approaches to calculate the convexity adjustment. 

The first is the Hull-White model, which has the advantage of being an efficient, closed-form solution. The downside is that it is insensitive to the volatility smile and doesn’t work for all products, resulting in pricing inconsistencies when applied to a derivatives portfolio. 

The second is the Carr-Madan replication formula, which takes smile dynamics into account but is computationally intensive, as the convexity adjustment needs to be calculated for each payment period. 

Skoufis’ approach, detailed in a recent Risk.net paper, aims to combine the best bits of the Hull-White and Carr-Madan models while overcoming their drawbacks – in other words, create an efficient solution that accounts for smile dynamics. 

“What I do in my particular approach is to use […] an accurate approximation, in which I boil down the convexity adjustment to be expressed as what I call a quadratic swap,” says Skoufis. 

This is done by taking the square of the netting value of the swap’s two legs – the floating and the fixed leg. That matches the quadratic form of the combination between the swap and the convexity adjustment, which is expressed in terms of another swap. Skoufis explains that this approach is intuitive because the value of the swap is obtained from the yield curve and the addition of a correction that involves this quadratic swap. 

In his paper, the closed-form solution developed to assess the convexity adjustment is applied to the Sabr model, the stochastic volatility model commonly used to price interest rate derivatives. 

In this podcast, Skoufis also shares his thoughts on the quantitative challenges posed by the transition away from Libor. While much of the groundwork for derivatives linked to the US secured overnight financing rate has been completed, more work remains to be done in Europe, where Euribor and €str are set to co-exist for the foreseeable future. And if a derivatives market on term RFRs were to develop, additional quant tools will be needed to price those products, he says. 

As for his own research, Skoufis plans to expand on his most recent paper and develop a new approach for calculating the average-rate convexity adjustment of RFR-based caps and floors. That could be the subject of a future podcast.

Index

00:00 Introduction and benchmark reforms

03:43 Arithmetic averaging of RFR swaps 

06:45 Convexity adjustment 

12:30 The Hull-White and Carr-Madan models

15:50 Skoufis’ closed-form solution

20:30 The Sabr model 

32:55 Convexity adjustments and the Sabr model

34:30 Building a volatility smile for €str

40:55 Research on caps and floors

To hear the full interview, listen in the player above, or download. Future podcasts in our Quantcast series will be uploaded to Risk.net. You can also visit the main page here to access all tracks, or go to the iTunes store or Google Podcasts to listen and subscribe.

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