On the inefficiency of Brownian motions and heavier tailed price processes

Recent literature has shown the existence of pathologies if one combines the most important models for pricing and hedging derivatives and coherent risk measures. There may exist portfolios (good deals) whose (return; risk) is as close as desired to (1; 􀀀1). This paper goes beyond existence properties and looks for explicit constructions and empirical tests. It will be shown that the good deal above may be a combination of European and digital options, very easy to replicate in practice. This theoretical nding will enable us to implement empirical experiments involving three international stock indices (S&P_500, Eurostoxx_50 and DAX) and three commodity futures (Gold, Brent and DJ 􀀀 UBSCI). According to the empirical results, the good deal always outperforms the underlying index/commodity. The good deal is built in full compliance with the standard Derivative Pricing Theory. Properties of classical pricing models totally inspire and lead the good deal construction. This is a very interesting di¤erence with respect to previous literature attempting to outperform a benchmark. Besides, the selected pricing models satisfy the existence of risk neutral probabilities such that self- nancing price processes become martingales. According to recent results, while local martin- gales characterize the absence of arbitrage, martingales characterize the existence of equilibrium. However, this equilibrium is di¢ cult to imagine, because for every portfolio traders can build a new one with identical price, higher return and lower risk. Perhaps dynamic arbitrage free pricing models contradict other important achievements of Financial Economics related to e¢ ciency and equilibrium, and further research is required to recover consistency.