On a Heath–Jarrow–Morton approach for stock options

Jan Kallsen () and Paul Krühner ()

Finance and Stochastics, 2015, vol. 19, issue 3, 583-615

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. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Heath–Jarrow–Morton; Option price surfaces; Lévy processes; 91B24; 91G20; G 12; G 13 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-015-0263-1

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