On a Heath-Jarrow-Morton approach for stock options

@article{Kallsen2015OnAH,
  title={On a Heath-Jarrow-Morton approach for stock options},
  author={Jan Kallsen and Paul Kr{\"u}hner},
  journal={Finance and Stochastics},
  year={2015},
  volume={19},
  pages={583-615}
}
This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to a related contribution by Carmona and Nadtochiy [7], the key parametrisation of our approach involves time-inhomogeneous Lévy 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… CONTINUE READING

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