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Windings of Planar Processes and Applications to the Pricing of Asian Options
Version 1
: Received: 22 October 2016 / Approved: 24 October 2016 / Online: 24 October 2016 (04:57:32 CEST)
How to cite: Vakeroudis, S. Windings of Planar Processes and Applications to the Pricing of Asian Options. Preprints 2016, 2016100097. https://doi.org/10.20944/preprints201610.0097.v1 Vakeroudis, S. Windings of Planar Processes and Applications to the Pricing of Asian Options. Preprints 2016, 2016100097. https://doi.org/10.20944/preprints201610.0097.v1
Abstract
Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.
Keywords
planar Brownian motion; complex-valued Ornstein-Uhlenbeck processes; Lévy~processes; Stable processes; windings; skew-product representation; Spitzer's Theorem; Bougerol's identity; Asian options; pricing
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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