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On a Heath-Jarrow-Morton approach for stock options

  • Jan Kallsen
  • Paul Kr\"uhner
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    This 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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    Paper provided by in its series Papers with number 1305.5621.

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    Date of creation: May 2013
    Date of revision: Aug 2013
    Handle: RePEc:arx:papers:1305.5621
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    1. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    2. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    3. 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.
    4. René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
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