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Multi-curve framework book: new edition in progress

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Subject: Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution, and Implementation It has been more than 10 years since I wrote the first edition of the multi-curve framework book. What happened in those 10 years? Why did it take me so long to start a new version? It took me roughly 10 years to write the first edition. The reason it took so long at that time, was that I did not know that I was writing it! I thought I was writing a couple of pages on an obscured and theoretical idea that there was not a `` one curve to rule them all '' but multiple curves. It turned out that it became the actual practice for very clear and important reasons. That was the excuse for the first edition, what is the excuse for the second edition? Since the first edition, many things happen, in particular: March 2015: BCBS - IOSCO: margin requirements for non-centrally cleared derivatives and mandatory variation margin July 2017: The future of LIBOR -- actually it...
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Treasury / Swap spreads are negative. And what?

In recent weeks there were several news articles related to the negative treasury/Swap spread. This is in particular the case of a Bloomberg article and a Zero Hedge blog . Some of the “information” in those notes are Swap rates are what companies, investors and traders pay to exchange fixed interest payments for floating ones. That rate falling below Treasury yields […]  is illogical in the eyes of most market observers, because it theoretically signals that traders view the credit of banks as superior to that of the U.S. government. It’s hard to overstate how illogical it is when swap spreads are inverted. That’s because it suggests that governments are less creditworthy than the very financial institutions they bailed out during the credit crisis just seven years ago. Let’s be clear, to me, those claims are purely wrong , nothing is “ illogical ” in negative swap spread. But why do I rant about that in the “multi-curve framework” blog? Because it is exactly the same that ...
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A 6 sigma event every 2 months!

“ So much or so much sigma, that is a mathematical impossibility. ” I have seen this sentence many times on LinkedIn or similar places. The supposed meaning of this sentence is that the probability of an event corresponding to x — with x being 3 or 6 or similar — standard deviations has a probability so small that it can be consider for all practical matter as impossible. These comments are based on a misunderstanding of what “ sigma ” represents together with a confusion between “normal distribution” and “any distribution”. I write this post with a discrete distribution notation but it can be extended easily — with a little bit of extra notations — to continuous distribution. Suppose that my distribution has n points with values a i and probabilities p i = 1/n ( i = 1, … , n ). The mean is m = sum i=1 n a i p i = 1/n sum i=1 n a i To simplify further my notations, I suppose that the mean is 0. The standard deviation is the square root of variance, with variance V = 1...
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