Spontaneous symmetry breaking of arbitrage

Abstract: We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered by a control parameter. We estimate the control parameter for momentum strategy with real historical data. The momentum strategy aided by symmetry breaking shows stronger performance and has a better risk measure than the naive momentum strategy in U.S. and South Korean markets.