The application of path integral for log return probability calculation

Conference of Theoretical Physics and Nonlinear Phenomena 2014: "From Universe to String's Scale"

Palupi, D.S.^1 ; Hermanto, A.^1 ; Tenderlilin, E.^2 ; Rosyid, M.F.^1

Jurusan Fisika, Fakultas Matemtika Dan Ilmu Pengetahuan Alam, Universitas Gadjah Mada, Indonesia^1

Fakultas Ekonomika Dan Bisnis, Universitas Gadjah Mada, Indonesia^2

关键词: Fokker-Plank equation;    Geometric Brownian motion;    Ornstein-Uhlenbeck process;    Path integral;    Path integral method;    Return probabilities;    Stochastic differential equations;    Stock price;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/539/1/012017/pdf
DOI  :  10.1088/1742-6596/539/1/012017

来源: IOP

【 摘 要 】

Log return probability has been calculated using path integral method. The stock price is assumed obeying the stochastic differential equation of a geometric Brownian motion and the volatility is assumed following Ornstein Uhlenbeck process. The stochastic differential equation of stock price and volatility lead to Fokker-Plank equation. The Fokker-Plank equation is solved using path integral method. Distribution of log return can be used to take the valuation ln return stock.