Almost-sure hedging with permanent price impact
B. Bouchard, G. Loeper, Y. Zou
TL;DR
This paper develops a model for super-hedging European options considering permanent price impact, deriving a quasi-linear PDE that guides optimal hedging strategies in a continuous-time setting.
Contribution
It introduces a novel super-hedging framework with permanent price impact and derives a corresponding quasi-linear pricing equation in viscosity sense.
Findings
Derived continuous-time trading dynamics from discrete policies.
Established a quasi-linear PDE for super-hedging with price impact.
Provided conditions for perfect hedging strategies when solutions are smooth.
Abstract
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models