Option Hedging with Smooth Market Impact

We consider a large investor hedging a long or short options position, whose trades generate adverse market impact. Unlike the complete-market or proportional transaction cases, the agent no longer finds it tenable to be perfectly hedged or even within a fixed distance of being hedged. Instead, he may find himself arbitrarily mishedged and optimally trades towards the classical Black-Scholes delta, with trading intensity proportional to the degree of mishedge and inversely proportional to illiquidity. Option hedging activity should cause a measurable increase or decrease in realized volatility, depending on whether sell-side traders are net long or short options. We illustrate the instability that can arise if the hedge strategy is applied carelessly with discrete time steps, and give a discrete-time formulation that avoids this instability.