SOFR and €STR Discounting: Forward Convexity from Discount-Rate Transition

Abstract

Due the the upcoming change in price alignment interest that is anticipated for SOFR and €STR, a new definition of the "hybrid" risk-neutral measure is developed, which is based on continuous reinvestment at the price alignment interest rate. A corresponding T-forward measure is defined, which is consistent with the treatment of cashflow obligations including bond prices and terminal payouts. Values obtained under the "hybrid" measure remain unchanged when combined with explicit modeling of the compensation payout at the transition time, in addition to describing any MTM change for uncompensated positions. This new measure also allows continuous construction of the forward curve in a way that is convexity-free up to and beyond the discounting transition, whereas the original pricing measure will see a sudden impact on the forward curve at the transition point. Lastly the "hybrid" measure provides a framework to model the forward curve convexity for trades with collateral agreements that do not transition simultaneously across different netting sets.

Keywords: SOFR, ESTR, €STR, discounting, PAI, convexity, discount, forward, curve, CME, LCH

JEL Classification: G12, G13, E43