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Modern Stochastics: Theory and Applications


Option pricing in time-changed Lévy models with compound Poisson jumps
Volume 6, Issue 1 (2019), pp. 81–107
Pub. online: 27 November 2018      Type: Research Article      Open accessOpen Access
Received
14 June 2018
Revised
3 September 2018
Accepted
7 November 2018
Published
27 November 2018

Abstract

The problem of European-style option pricing in time-changed Lévy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the time-changed Lévy models, the variance-gamma and the normal-inverse Gaussian models are discussed. Exact formulas are given for the price of digital asset-or-nothing call option on extra asset in foreign currency. The prices of simpler options can be derived as corollaries of our results and examples are presented. Various types of dependencies between stock prices are mentioned.

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© 2019 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Lévy process change of time compound Poisson process digital option variance-gamma process hypergeometric function

MSC2010
6008 60G44 60G51 60H30 60J75

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