Prices of Options as Opinion Dynamics of the Market Players with Limited Social Influence

Abstract: The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the value of a stock. The model presented in this paper is suited for pricing of options and was verified against real market data. The model allows deriving the parameters of market players from available real market data, especially maximum possible correlation (herding) and anti-correlation between the players' opinions. The deviations of market prices from those predicted by the Black-Scholes model, such as smile and skew implied volatilities, are interpreted as the current values and limits of social influence of the market players, respectively. To the best of our knowledge, this is the first work that discriminates skew and smile phenomena. Our approach unifies and develops a further connection between trading, voters' model, and statistical physics analogies of opinion dynamics.