The calculation of probability distribution of return in IDX using path integral method

The Probability distribution of return in IDX (Indonesia Stock Exchange) has been calculated. We assume the evolution of the stock price as geometrical Brownian process and the volatility follows the Ornstein-Uhlenbeck process as in Heston model. The equations of stock and volatility lead to Fokker-Planck equation and we solved this equation by making use of path integral. We fit the probability distribution theoretically with the probability of Jakarta Islamic Index, Jakarta Composite Index, and LQ45. Jakarta Islamic Index, Jakarta Composite Index and LQ45 are indexed in IDX