Financial institutions need to price a huge number of instruments every day, and each of these instruments is generally priced according to models calibrated on financial data. The key issue, however, is that different institutions price the same instruments using different models and data, i.e. different approximations. Such a heterogeneous picture might lead to a system of inconsistent prices, or, in other words, to arbitrage opportunities, i.e. the emergence of strategies yielding a risk free profit. In this talk I will address this issue in the stylized framework of a random economy, where the differences in the pricing models are introduced as differences in the probability measures used to price different financial instruments. Depending on the variability of such measures and the number of assets, the market may be either in an arbitrage free state or in a state where arbitrage opportunities actually arise. The problem will be analyzed borrowing techniques from the statistical physics of disordered systems: a general solution for the arbitrage region volume in the model's parameter space will be derived and discussed, eventually providing numerical evidence for some specific examples.