Pathwise no-arbitrage in a class of Delta hedging strategies
Mathematical Finance
2016-06-16 v4 Probability
Abstract
We consider a strictly pathwise setting for Delta hedging exotic options, based on F\"ollmer's pathwise It\=o calculus. Price trajectories are -dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space. Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.
Keywords
Cite
@article{arxiv.1511.00026,
title = {Pathwise no-arbitrage in a class of Delta hedging strategies},
author = {Alexander Schied and Iryna Voloshchenko},
journal= {arXiv preprint arXiv:1511.00026},
year = {2016}
}