On a Heath-Jarrow-Morton approach for stock options
AbstractThis paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by Carmona and Nadtochiy (2009) and related to the recent contribution Carmona and Nadtochiy (2012) by the same authors, the key parametrisation of our approach involves time-inhomogeneous L\'evy processes instead of local volatility models. We provide necessary and sufficient conditions for absence of arbitrage. Moreover we discuss the construction of arbitrage-free models. Specifically, we prove their existence and uniqueness given basic building blocks.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1305.5621.
Date of creation: May 2013
Date of revision: Aug 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-04 (All new papers)
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- René Carmona & Sergey Nadtochiy, 2011. "Tangent Models As A Mathematical Framework For Dynamic Calibration," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 107-135.
- René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
- René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
- Denis Belomestny & Markus Reiß, 2006.
"Spectral calibration of exponential Lévy models,"
Finance and Stochastics,
Springer, vol. 10(4), pages 449-474, December.
- Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models ," SFB 649 Discussion Papers SFB649DP2006-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models ," SFB 649 Discussion Papers SFB649DP2006-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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