The Ornstein-Uhlenbeck Process and Variance Gamma Process: Parameter Estimation and Simulations

The Variance Gamma (VG) model has been increasingly used as an alternative to the standard geometric Brownian motion (GBM) model in modelling asset prices. We consider a F(a, 0) Ornstein-Uhlenbeck process and build a continuous sample path Variance-Gamma (VG) model with five parameters (mu, 6, a, a, 0): location (mu), symmetry (6), volatility (a), and shape (a) and scale (0). The simulations of the five parameters Variance-Gamma (VG) Process are performed after fitting the VG model to the underlying distribution of the daily SPY ETF return.