The physics of stochastic processes applied to binary options in financial markets

Abstract

The analogy between the problem of a player who bets money iteratively in a game of chance and a random walker in one dimension with an absorbing boundary is well known. These and other connections between finance and physics motivated the emergence of the field of econophysics in the 1990s. Since the subject matter is still not well known at the level of undergraduate physics programs, here we first review some basic concepts, such as martingales, financial derivatives and stock options. Our objectives are the following: (i) to explain how binary options work; (ii) to simulate stochastically the behavior of the balance sheet curve for different hit rates; (iii) to run tests of the success rates for the stochastic oscillator indicator in financial time series of historical data. This indicator is widely used by binary option traders, so it is an ideal illustrative example. Our results show that it is difficult to obtain consistent profits, even using strategies based on martingales or "Soros" leveraging to recover previous losses. The empirical characterization of this difficulty may help to make clearer the unpredictability and high degree of complexity of the behavior seen in financial markets.