Badly Arbitraged Markets and Negative Martingale Measures

Abstract

In this paper, we seek to measure the impact of arbitrage opportunities on some key results of asset pricing theory. We do this by showing how a market that is viable, but potentially badly arbitraged, can exist if the agents' preferences is modified. In this case, the pricing measure is not necessarily positive and can no longer be treated as a risk-neutral probability. Unless such arbitrage opportunities are of the cash-and-carry kind, prices remain martingale under this potentially negative measure. This engenders generic phenomena such as information loss and price confinement zones. To better understand these phenomena, we construct an example of a martingale under a signed measure. In conclusion, we remind an empirical test for arbitrage detection, which we apply to CME options on the S\&P 500 index options during the turbulent aftermath of the bankruptcy of Russia.