Pricing European options and risk measurement under exponential Lévy models - a practical guide

Khaled Salhi 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : This paper provides a thorough survey of the European option pricing, with new trends in the risk measurement, under exponential Lévy models. We develop all steps of pricing from equivalent martingale measures construction to numerical valuation of the option price under these measures. We then construct an algorithm, based on Rockafellar and Uryasev representation and fast Fourier transform, to compute Risk indicators, like the VaR and the CVaR of derivatives. The results are illustrated with an example of each exponential Lévy class. The main contribution of this paper is to build a comprehensive study from the theoretical point of view to practical numerical illustration and to give a complete characterization of the studied equivalent martingale measures by discussing their similarity and their applicability in practice. Furthermore, this work proposes applications to the Fourier inversion technique in risk measurement.
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Article dans une revue
International Journal of Financial Engineering, World Scientific, 2017, 2 (2-3), 1750016 (36 p.). 〈10.1142/S2424786317500165〉
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https://hal.inria.fr/hal-01322698
Contributeur : Khaled Salhi <>
Soumis le : vendredi 18 novembre 2016 - 17:24:26
Dernière modification le : samedi 6 octobre 2018 - 01:16:21
Document(s) archivé(s) le : mardi 21 mars 2017 - 05:38:36

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Khaled Salhi. Pricing European options and risk measurement under exponential Lévy models - a practical guide. International Journal of Financial Engineering, World Scientific, 2017, 2 (2-3), 1750016 (36 p.). 〈10.1142/S2424786317500165〉. 〈hal-01322698v2〉

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