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Abstract
We characterize strictly arbitrage-free markets of European options where only a discrete set of options is traded. We then construct martingales which reprice all given options and which are ‘most expensive’ among all martingales with this property. We also present algorithms to adjust real-life market data and to construct expensive martingales while taking into account additional ‘weak’ information: estimated prices of more exotic products such as, for example, forward started options.
Acknowledgment
I want to express my gratitude to Dr. Marcus Overhaus, Prof. Dr. Alexander Schied and the whole Deutsche Bank GME Quantitative Products Analytics team, http://www.dbquant.com. This work has been developed as part of my work in this team and of my doctoral dissertation at the Technical University Berlin with Professor Schied.
The author was supported by the DFG Research Center Matheon ‘Mathematics for key technologies’ (FZT 86).
Notes
† In a discrete setting, they coincide, see Harrison and Pliska (Citation1981).
‡ We call a martingale a ‘Markov martingale’ if it has the Markov property, i.e. if
for all bounded F.