We consider the problem of a trader hedging a large options position. We use a realistic proportional market impact cost model, as is commonly used in optimal execution problems, rather than the bid-ask spread model which has been previously used. We also include overnight risk, which is important for an intraday hedge position. Our solutions solve a “pursuit problem”, in which the actual hedge position moves smoothly in the direction of the perfect Black-Scholes hedge. We also obtain an expression for the modified volatility of the underlying caused by the hedge activity: if the hedger is long the option then volatility decreases and conversely if he is short (Joint work with Michael Li, Princeton University).