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Finance and Stochastics

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01-01-2016

Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

Authors: José E. Figueroa-López, Sveinn Ólafsson

Published in: Finance and Stochastics | Issue 1/2016

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Abstract

In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.

previous article Dynamic optimal execution in a mixed-market-impact Hawkes price model

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In the case when \(S_{t}=S_{0}e^{X_{t}+V_{t}}\) contains a nonzero continuous component \(V\), we consider instead an extension of \(\varOmega=\mathbb{D}([0,\infty),\mathbb{R})\) that accommodates the independent Wiener processes \(W^{1}\) and \(W^{2}\).

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Title: Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility
Authors: José E. Figueroa-López
Sveinn Ólafsson
Publication date: 01-01-2016
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 1/2016
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-015-0281-z

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