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Variance Gamma (nonlocal) equations
Modern Stochastics: Theory and Applications, 2023 Some equations are provided for the Variance Gamma process using the definition other than that based on a time-changed Brownian motion. A new nonlocal equation is obtained involving generalized Weyl derivatives, which is true even in the drifted case ...
Fausto Colantoni
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Pricing with Variance Gamma Information [PDF]
Risks, 2020 In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration {Ft}t≥0 is generated by an information process {ξt}t≥0 defined in such a way that at some fixed time T an FT-measurable random variable XT is “revealed”.
Lane P. Hughston +1 more
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The variance-gamma ratio distribution [PDF]
Comptes Rendus. Mathématique, 2023 Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived.
Gaunt, Robert E., Li, Siqi
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The Variance-Gamma Product Distribution. [PDF]
Results MathAbstract We derive the exact probability density function of the product of N independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and characteristic function, as well
Gaunt RE, Li S, Sutcliffe HL.
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The Variance Gamma++ process and applications to energy markets [PDF]
Applied Stochastic Models in Business and Industry, 2022 AbstractThe purpose of this article is to introduce a new Lévy process, termed the Variance Gamma++ process, to model the dynamics of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is obtained by applying the self‐decomposability of the gamma law.
Matteo Gardini +2 more
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An Expanded Local Variance Gamma Model [PDF]
Computational Economics, 2020 38 pages, 8 figures, 5 ...
P. Carr, A. Itkin
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Media Statistika, 2022 The Option is widely applied in the financial sector. The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement.
Abdul Hoyyi +2 more
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Mathematics, 2021 Recently, maintaining a complex mechanical system at the appropriate times is considered a significant task for reliability engineers and researchers. Moreover, the development of advanced mechanical systems and the dynamics of the operating environments
Marwa Belhaj Salem +2 more
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Pricing and Hedging Index Options under Mean-Variance Criteria in Incomplete Markets
Computation, 2023 This paper studies the portfolio selection problem where tradable assets are a bank account, and standard put and call options are written on the S&P 500 index in incomplete markets in which there exist bid–ask spreads and finite liquidity.
Pornnapat Yamphram +2 more
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Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros [PDF]
PeerJ, 2022 The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess ...
Wansiri Khooriphan +2 more
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