The Present of Futures: Valuing Eurodollar-Futures Convexity Adjustments in a Multi-Curve World

Abstract

Futures convexity adjustments in the multi-curve world depend on: i) the distribution of forward LIBORs, ii) the distribution of OIS rates, and iii) the correlation between LIBORs and OIS rates. In this article, we introduce a new multi-curve framework for pricing futures convexity adjustments. We assume that forward LIBORs follow a one-factor shifted-lognormal LMM, and that OIS rates evolve according to a general one-factor Cheyette (1992) model. We will consider two particular cases: 1) OIS rates follow a one-factor Hull-White (1990) model; 2) the LIBOR-OIS basis volatility is minimal, which includes the sub-case of deterministic basis when LIBOR and OIS curves are perfectly correlated. We will derive explicit convexity adjustments in both cases, and analyze the impact of the cap skew in their valuation. We will show that the extent a cap smile affects futures pricing depends on the chosen OIS dynamics, or equivalently on the assumed behavior of the LIBOR-OIS basis.

Keywords: Eurodollar Futures, Convexity Adjustments, Multi-Curve Models

JEL Classification: C22, E43, G13