On Regret and Options - A Game Theoretic Approach for Option Pricing†

We study the link between the game theoretic notion of ’regret minimization’ and robust option pricing. We demonstrate how trading strategies that minimize regret also imply robust upper bounds for the prices of European call options. These bounds are based on ’no-arbitrage’ and are robust in that they require only minimal assumptions regarding the stock price process. We then focus on the optimal bounds and demonstrate that they can be expressed as a value of a zero sum game. We solve for the optimal volatility-based bounds in closed-form, which in turn implies the optimal regret minimizing trading strategy. † We thank Sergiu Hart for helpful discussion and seminar participants at Berkeley (IEOR), Tel Aviv university, Hebrew University and Stanford for useful comments.