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*Amam Taufiq Hidayat  -  Departemen Matematika, FMIPA, Universitas Gadjah Mada, Indonesia
Subanar Subanar  -  Departemen Matematika, FMIPA, Universitas Gadjah Mada, Indonesia
Open Access Copyright (c) 2020 MEDIA STATISTIKA under

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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

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Keywords: Levy Process; Ornstein-Uhlenbeck process; BNS Gamma Ornstein Uhlenbeck Model

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