Perturbation analysis of sub/super hedging problems
Abstract
We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No-arbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite-dimensional sub- and super-hedging problems. With a view towards applications, we show how duality is preserved when reducing these problems over finite-dimensional bases. We finally perform a rigorous perturbation analysis of those linear programming problems, and highlight numerically the influence of smile extrapolation on the bounds of exotic options.
Keywords
Cite
@article{arxiv.1806.03543,
title = {Perturbation analysis of sub/super hedging problems},
author = {Sergey Badikov and Mark H. A. Davis and Antoine Jacquier},
journal= {arXiv preprint arXiv:1806.03543},
year = {2021}
}
Comments
26 pages. Forthcoming in Mathematical Finance