2020/04/18 by Ivan Arraut, Arraut, Ivan, Alan Au +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Financial Markets and Investment Strategies #Stochastic processes and financial applications #q-fin.GN
paper · pdf · doi:10.48550/arxiv.2004.11270
14 pages, submitted to Physica A
arxiv created 2020/04/18 · arxiv updated 2020/04/24
We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum condition when we express the financial equations in the Hamiltonian form. We then show that the symmetry under the changes of the prices is spontaneously broken in general and the symmetry under changes in the volatility, for the case of the Merton-Garman (MG) equation, is also spontaneously broken. This reproduces a vacuum degeneracy for the system. In this way, we find the conditions under which, the martingale condition can be considered to be a non-degenerate vacuum. This gives us a surprising connection between spontaneous symmetry breaking and the flow of information through the boundaries for the financial systems. Subsequently, we find an extended martingale condition for the MG equation, depending not only prices but also on the volatility and finally, we show what happens if we include additional non-derivative terms on the Black Scholes and on the MG equations, breaking then some other symmetries of the system spontaneously.