The Ornstein-Uhlenbeck process and variance gamma process: parameter estimation and simulations. (English) Zbl 07829891
Summary: 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 \(\Gamma (\alpha, \theta)\) Ornstein-Uhlenbeck process and build a continuous sample path Variance-Gamma (VG) model with five parameters \((\mu, \delta, \sigma, \alpha, \theta)\): location \((\mu)\), symmetry \((\delta)\), volatility \((\sigma)\), and shape \((\alpha)\) and scale \((\theta)\). 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.
MSC:
| 62M05 | Markov processes: estimation; hidden Markov models |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
| 60G10 | Stationary stochastic processes |
Keywords:
Ornstein-Uhlenbeck (OU) process; stochastic volatility (SV) model; variance gamma (VG) modelReferences:
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