Convexity adjustment and discounting transition

The collateral transition from EFFR to SOFR as planned by LCH and CME in October 2020 generates an exotic convexity adjustment on USD-LIBOR payments with respect to the absence of collateral transition. This convexity adjustment is already incorporated in the cleared swap pricing. This adjustment leads to many questions. Some of them are
  1. What inverse convexity should be introduced to price OTC bilateral LIBOR swaps from cleared LIBOR swaps?
  2. Why was this adjustment not described by CCPs in their transition documents and no compensation for it was proposed?
  3. What is the order of magnitude of the convexity adjustment?
In some sense, the third question may contain an answer for the first two. If the order of magnitude is negligible in practice, the answer to the first two question probably is: we don't care!

I have submitted a paper proposing a (relatively simple) theoretical computation of the convexity adjustment and an estimate of the order of magnitude. The results indicate that the order of magnitude may not be negligible in practice, opening the door to ask the first two questions. Some of the foundations of that papers have already been published in a working paper: Discounting Transition: Big Bang Impacts (https://ssrn.com/abstract=3530464).

The convexity adjustment in the current version of the paper is based on two collateral rates modeled with (correlated) Hull-White models and the LIBOR rate modeled with a version of the hybrid multi-curve model that I described a couple of years ago. I'm also working on improvements based on a G2++ model.

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