Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/275151 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 16 [Issue:] 1 [Article No.:] 55 [Year:] 2023 [Pages:] 1-28
Publisher: 
MDPI, Basel
Abstract: 
The paper builds a Variance-Gamma (VG) model with five parameters: location (μ), symmetry (δ), volatility (σ), shape (»), and scale (θ); and studies its application to the pricing of European options. The results of our analysis show that the five-parameter VG model is a stochastic volatility model with a Γ(»,θ) Ornstein-Uhlenbeck type process; the associated Lévy density of the VG model is a KoBoL family of order ν=0, intensity », and steepness parameters δσ2−δ2σ4+2θσ2 and δσ2+δ2σ4+2θσ2; and the VG process converges asymptotically in distribution to a Lévy process driven by a normal distribution with mean (μ+»θδ) and variance »(θ2δ2+σ2θ). The data used for empirical analysis were obtained by fitting the five-parameter Variance-Gamma (VG) model to the underlying distribution of the daily SPY ETF data. Regarding the application of the five-parameter VG model, the twelve-point rule Composite Newton-Cotes Quadrature and Fractional Fast Fourier (FRFT) algorithms were implemented to compute the European option price. Compared to the Black-Scholes (BS) model, empirical evidence shows that the VG option price is underpriced for out-of-the-money (OTM) options and overpriced for in-the-money (ITM) options. Both models produce almost the same option pricing results for deep out-of-the-money (OTM) and deep-in-the-money (ITM) options.
Subjects: 
stochastic volatility
Lévy process
Ornstein-Uhlenbeck process
infinitely divisible distribution
Variance-Gamma (VG) model
function characteristic
Esscher transform
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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