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Finance and Stochastics

, Volume 19, Issue 3, pp 583–615 | Cite as

On a Heath–Jarrow–Morton approach for stock options

  • Jan KallsenEmail author
  • Paul Krühner
Article

Abstract

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 (Finance Stoch. 13:1–48, 2009) and related to the recent contribution (Finance Stoch. 16:63–104, 2012) by the same authors, the key parameterisation 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 and uniqueness given basic building blocks.

Keywords

Heath–Jarrow–Morton Option price surfaces Lévy processes 

Mathematics Subject Classification

91B24 91G20 

JEL Classification

G 12 G 13 

Notes

Acknowledgements

We should like to thank the anonymous referees and the Associate Editor for various useful comments and suggestions.

Supplementary material

780_2015_263_MOESM1_ESM.pdf (288 kb)
(PDF 288 kB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsKiel UniversityKielGermany
  2. 2.Financial and Actuarial MathematicsVienna University of TechnologyViennaAustria

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