Artikel
Pricing European options under stochastic volatility models: Case of five-parameter variance-gamma process
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.
- Language
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Englisch
- Bibliographic citation
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Journal: Journal of Risk and Financial Management ; ISSN: 1911-8074 ; Volume: 16 ; Year: 2023 ; Issue: 1 ; Pages: 1-28
- Classification
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Management
- Subject
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stochastic volatility
Lévy process
Ornstein-Uhlenbeck process
infinitely divisible distribution
Variance-Gamma (VG) model
function characteristic
Esscher transform
- Event
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Geistige Schöpfung
- (who)
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Nzokem, Aubain Hilaire
- Event
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Veröffentlichung
- (who)
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MDPI
- (where)
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Basel
- (when)
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2023
- DOI
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doi:10.3390/jrfm16010055
- Handle
- Last update
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10.03.2025, 11:41 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Nzokem, Aubain Hilaire
- MDPI
Time of origin
- 2023
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