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V@R and minimal tick value

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...
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Multi-curve framework book new edition: endorsement by Andrea Pallavicini

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...
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Negative Swap / Government Spread: A SOFR definition impact

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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 ...
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Multi-curve framework book new edition: endorsement by Damiano Brigo

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. Marc Henrard has written a much needed second edition of his successful and popular multi-curve book. After a number of events, including the so-called LIBOR end hit the markets, and new types of contracts with new types of rates have appeared, together with some instances of survival of the old rates, a book like this has been much needed for the quant community and beyond. I will personally recommend this book to my MSc students who need to navigate the nuance of current interest rate markets. Marc has done a massive work of absorbing the changes introduced both by public institutions and the quant community in a coherent narrative. The boo...
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Taxe sur les plus-values en Belgique

La Belgique se prépare à mettre en place une taxe sur les plus-values (réalisées). Les textes exact n’ont pas encore été votés, il n’y a pas encore de précision sur le mécanisme exact. J’ai essayé de comprendre le mécanisme général, mais j’ai encore pas mal de questions. J’en indique quelques-unes ci-dessous. J’espère que les réponses seront dans le texte final. A défaut, le parlement peut toujours me contacter pour des conseils. Pour les actions en portefeuille à la date de l’entrée en vigueur de la loi (2026-01-01), les plus-values seront calculées sur base de la valeur à cette date. Comment est calculée la valeur d’une action non cotée? Cela doit être disponible pour une action à propos de laquelle le détenteur n’a aucune information (outre le fait d’en être le détenteur d’actions). Les employés de start-up reçoivent souvent des actions d’une société mère qui a une résidence fiscale non-belge. Quelle est la notion de plus-value après l'exercice d’une option? Si j’exerce un cal...
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Multi-curve framework book new edition: endorsement by Marco Bianchetti

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. This is the book I would have loved to write, but now that I have it in front of me, I realize I would not have matched Marc Henrard's excellence. All the essential aspects needed to understand modern interest rate modelling theory, as well as to apply it in everyday financial practice, are clearly explained with a rigorous yet practical approach. Definitely, it is one of the books that every practitioner of quantitative finance should read and keep at hand. Marco Bianchetti Head of Market and Counterparty Risk IMA Methodologies, Market and Financial Risk Management, Intesa Sanpaolo, Milan Adjunct Professor of Advanced Interest Rate...
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Multi-curve book: About the Book

The multi-curve book continue its march to production. The final proofs are expected for the end of October for a book publication in November. Find below the book's synopsis. About the Book A new standard in interest rate modelling, called the multi-curve framework, emerged after the financial crisis. The framework covers two important market features: the collateralization of derivative trades and the spread between different rate benchmarks. This book starts from the collateral mechanisms and builds the full framework from the foundations through all the technical and financial details. It kicks off with the collateral discounting in all its variants: domestic cash, foreign cash, or other assets and then introduces the different benchmarks and their associated spreads. Following the discontinuation of certain benchmarks, part of the book is dedicated to the transition and the emergence of the overnight benchmark dominance in certain currencies. Based on the theoretical fram...
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