On a Heath-Jarrow-Morton approach for stock options



Kallsen, Jan and Kruehner, Paul
(2015) On a Heath-Jarrow-Morton approach for stock options. Finance and Stochastics, 19 (3). 583 - 615.

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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.

Item Type: Article
Uncontrolled Keywords: Heath-Jarrow-Morton, Option price surfaces, Levy processes
Depositing User: Symplectic Admin
Date Deposited: 10 Dec 2018 09:37
Last Modified: 09 Jan 2021 04:32
DOI: 10.1007/s00780-015-0263-1
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3029737