Option pricing in time-changed Lévy models with compound Poisson jumps
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-inver...
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| Format: | Article |
| Language: | English |
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VTeX
2018-11-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/18-VMSTA124 |
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doaj-cee2d7e580f248678d3b199513e653602020-11-25T00:41:04ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542018-11-01618110710.15559/18-VMSTA124Option pricing in time-changed Lévy models with compound Poisson jumpsRoman V. Ivanov0Katsunori Ano1Laboratory of Control under Incomplete Information, Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russian FederationDepartment of Mathematical Sciences, Shibaura Institute of Technology, Tokyo 135-8548, JapanThe 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.https://www.vmsta.org/doi/10.15559/18-VMSTA124Lévy processchange of timecompound Poisson processdigital optionvariance-gamma processhypergeometric function |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Roman V. Ivanov Katsunori Ano |
| spellingShingle |
Roman V. Ivanov Katsunori Ano Option pricing in time-changed Lévy models with compound Poisson jumps Modern Stochastics: Theory and Applications Lévy process change of time compound Poisson process digital option variance-gamma process hypergeometric function |
| author_facet |
Roman V. Ivanov Katsunori Ano |
| author_sort |
Roman V. Ivanov |
| title |
Option pricing in time-changed Lévy models with compound Poisson jumps |
| title_short |
Option pricing in time-changed Lévy models with compound Poisson jumps |
| title_full |
Option pricing in time-changed Lévy models with compound Poisson jumps |
| title_fullStr |
Option pricing in time-changed Lévy models with compound Poisson jumps |
| title_full_unstemmed |
Option pricing in time-changed Lévy models with compound Poisson jumps |
| title_sort |
option pricing in time-changed lévy models with compound poisson jumps |
| publisher |
VTeX |
| series |
Modern Stochastics: Theory and Applications |
| issn |
2351-6046 2351-6054 |
| publishDate |
2018-11-01 |
| description |
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. |
| topic |
Lévy process change of time compound Poisson process digital option variance-gamma process hypergeometric function |
| url |
https://www.vmsta.org/doi/10.15559/18-VMSTA124 |
| work_keys_str_mv |
AT romanvivanov optionpricingintimechangedlevymodelswithcompoundpoissonjumps AT katsunoriano optionpricingintimechangedlevymodelswithcompoundpoissonjumps |
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1725287418136887296 |