Perfect hedging under endogenous permanent market impacts
Mathematical Finance
2017-02-07 v1 Probability
Pricing of Securities
Abstract
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering, a trader is no more price taker as any trade has a permanent market impact via an effect to the supplier's inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting the corresponding pricing and hedging can be done by solving a semi-linear PDE.
Keywords
Cite
@article{arxiv.1702.01385,
title = {Perfect hedging under endogenous permanent market impacts},
author = {Masaaki Fukasawa and Mitja Stadje},
journal= {arXiv preprint arXiv:1702.01385},
year = {2017}
}