An Optimal Timing Approach to Option Portfolio Risk Management

Investors often control risk exposure by trading options. This article studies the optimal strategy for liquidating an option position. Under both complete and incomplete market settings, we quantify the value of optimally timing to liquidate, and identify the situations where it is optimal to hold the option position through expiration. Numerical illustration of the non-trivial liquidation timing is provided for the cases of a straddle and a butterfly, along with a sensitivity analysis on the drift of the underlying stock. We also give an overview of option liquidation in incomplete markets with stochastic volatility