Arbitrage opportunities in misspecified stochastic volatility models

There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics are classical Black-Scholes ones, we give a new interpretation of the butterfly and risk reversal contracts in terms of their performance for volatility arbitrage. Our results are illustrated by a numerical example including transaction costs.