2013/05/24 by Jan Kallsen, Kallsen, Jan, Paul Krühner +1 · 5 citations
Economics, Econometrics and Finance · Mathematics · #91B24 #91G20 #Arbitrage #Complex Systems and Time Series Analysis #Computer science #Econometrics #Economics #FOS: Economics and business #Financial Risk and Volatility Modeling #Financial economics #Key (lock) #Mathematical economics #Mathematics #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #Uniqueness #Volatility (finance) #msc:91B24 #msc:91G20 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1305.5621
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2013/05/24 · arxiv created 2013/08/21 · arxiv updated 2013/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 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.