Showing 1 - 10 of 13
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,...
Persistent link: https://www.econbiz.de/10013003111
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...
Persistent link: https://www.econbiz.de/10012987035
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...
Persistent link: https://www.econbiz.de/10013229297
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...
Persistent link: https://www.econbiz.de/10013323254
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....
Persistent link: https://www.econbiz.de/10012835255
This paper addresses the problem of specifying boundary conditions for Fokker-Planck PDE for reflecting diffusions arising in finance. Main focus is the CIR model, but techniques presented are readily applicable to other models with reflecting boundaries
Persistent link: https://www.econbiz.de/10012723586
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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...
Persistent link: https://www.econbiz.de/10012973640
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
Persistent link: https://www.econbiz.de/10013406186
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