PERSAMAAN DIFERENSIAL ORNSTEIN-UHLENBECK DALAM PERAMALAN HARGA SAHAM

Abstract

Geometric Brownian motion is one of the most widely used stock price model. One of the assumptions that is filled with stock return volatility is constant. Gamma Ornstein-Uhlenbeck process a model to describe volatility in finance. Additionally, Gamma Ornstein-Uhlenbeck process driven by Background Driving Levy Process (BDLP) compound Poisson process and the marginal law of volatility follows a Gamma distribution. Barndorff-Nielsen and Shepard (BNS) Gamma Ornstein-Uhlenbeck model can to sample the process for the stock price with volatility follows Gamma Ornstein-Uhlenbeck process. Based on these, the simulation result are compared BNS Gamma Ornstein-Uhlenbeck model with geometric Brown motion for Standard and Poor (SP) 500 stock data. Simulation result give BNS Gamma Ornstein-Uhlenbeck model and Geometric Brownian motion a Root Mean Square Error (RMSE) are 0,13 and 0,24 respectively. These result indicate that the BNS Gamma Ornstein-Uhlenbeck model gives a more accurate than Geometric Brownian motion

Keywords

• levy process
• ornstein-uhlenbeck process
• bns gamma ornstein uhlenbeck model