Marc Henrard - Multi-curve framework

L'inflation belge accélère à 2,4% en novembre. Titre d'un article de l'Echo aujourd'hui . Dérivée troisième, Ah ! Que J’aime entendre ta voix ! L’inflation est le changement de prix, une accélération est la dérivée seconde de la position d’inflation. Nous sommes donc en présence d’un article sur la dérivée troisième des prix comme fonction du temps. Malheureusement la première ligne de l’article déçoit immédiatement les fans de la dérivée troisième, car elle indique: L'inflation [...] est repartie à la hausse. Seulement une dérivée seconde! Ce que l’article n’indique pas est que l’inflation généralement commentée est l’inflation annuelle. Quand on compare l'inflation d'"octobre 2025" à l'inflation de "novembre 2025", il y a 11 mois en commun. Par conséquent, on compare novembre 2025 — qui entre dans la période annuelle — à novembre 2024 — qui en sort. Pour comprendre ce qui ce passe, il faut aller à la source (Stabel) mais mal...

A Value-at-Risk (VaR) methodology is a technique to estimate the maximum loss at a given time horizon that is exceeded only at a certain probability level. Several methodologies are used to obtain those estimations and a lot of them are based on “scenarios”. They can be historical data inspired, stress tests or Monte Carlo. Those methodologies are often used to compute Initial Margin (IM) related to exchange traded portfolios. The instruments in exchange trades setup have standardized terms and conditions, including a “tick value” or “minimal increment” which indicates the precision of the price quotation mechanism. This is often one cent on prices and one basis point for interest rates. I have been involved in many VaR and IM methodologies over the past years: development, replication, validation. One question that I have been asked several times with different flavours is: How should the methodology account for tick value in the scenarios? Should the price generated by the scena...

Different experts in interest rate modelling were kind enough to write an endorsement for the multi-curve new edition book. Part of them are displayed on the back-cover (there is not enough space to display the full texts there). I will publish on this blog the longer versions of them between now the actual book's publication in November December. A decade ago, this book did not just introduce the essential multi-curve framework; it also laid its foundations with rigorous clarity, recognizing the pitfalls of simply adapting old "one-curve" approaches. Now, in its vital second edition, the author delivers an even more indispensable resource, profoundly addressing the market shifts that have redefined interest rate modeling. This edition is a direct response to critical changes like BCBS-IOSCO margin requirements and, most importantly, the end of LIBOR and the benchmark transition. The book's strength lies in its axiomatic approach, providing solid proofs and clea...

Negative government bond spreads have been a puzzle for some people for a long time. The question has been stated in some places as `` How can the banks borrow at a lower rate than the government? ''. I have already partially given my point of view about that issue in a blog 10 years ago . That was in the context of the LIBOR swaps, but it is still true in the SOFR case. Now I want to add some technical details for the SOFR OIS case. To some extent, I claim that the swap spread have to be negative! SOFR-OIS swap / government spreads In this analysis, I'm using the results of the multi-curve framework in a loose sense. I'm using expected values, without clarifying in which measure they are and extended the results to government bonds. The goal is to indicate that the ISDA definition of SOFR (introduced below) used in swaps may have an hidden impact on swap spreads. For this simplified approach, I'm presenting the impact only for zero-coupon bonds. The notation ...