We revisit the classical problem of convergence of the maximum of cumulative sums of IID random variables by introducing ideas from the Karamata's celebrated proof of the Hardy-Littlewood Tauberian Theorem [J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes,...

We revisit the problem addressed in Gatarek et al. and derive an algorithm for determining the Chayette local volatility based on the options marked for fixed-tenor rolling maturity swaptions. Apart from the discretization error inherent in calibration-simulation procedures, the formula...

We provide an alternative proof of monotonicity of normalizing volatility transforms (NVTs) due to Fukasawa (2012), and then obtain a general formula for volatility surface for which the NVTs are increasing. This is used to obtain several results related to butterfly arbitrage and asymptotic...

Motivated by the recent Log Moment formula of \cite{raval_jacquier21}, we look at the power of absolute Log Contract $|\log(S_T/F_T)|^q$, $q\geq 1$, and derive its corresponding replicating strip of Vanilla options. Unlike the standard Log Contract where the Delta of the replicating portfolio...

This, somewhat unusual collection of problems in Measure-Theoretic Probability and Stochastic Analysis, should have been more appropriately called: ``The Problems I Like". For the material borrowed from the existing literature, full references and occasional historical remarks are provided....

We look at the real positive (semi)definite matrix completion problem from the convex optimization viewpoint.The problem is introduced via relative entropy minimization, transformed into the standard max-det from, and conditions are sought for existence of positive definite and positive...

At present, the most liquidly traded listed options on the crypto underlying are so-called inverse vanilla options. In this note we show how such contacts are just regular vanilla options considered under the well-known martingale measure making underlying the numeraire

In this work we provide generalization and unification of several moment formulae: the Lee Moment Formula of Lee (2004), Log Moment Formula of Raval and Jacquier (2021), and the modified Piterbarg conjecture of Gulisashvili (2012). We approach the problem via investigating asymptotic behavior of...