A generalized hyperbolic model for a risky asset with dependence. (English) Zbl 1471.91566
Summary: We present a construction of the Generalized Hyperbolic (GH) subordinator model for a risky asset with dependence. The construction of the subordinator (activity time) process is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. It unifies, on the basis of self-decomposability of the Generalized Inverse Gaussian (GIG) distribution, the construction of the various special cases of the GH subordinator class, such as the Variance Gamma, normal inverse Gaussian, hyperbolic and, especially, \(t\) distributions. An option pricing formula for the proposed model is derived.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60G10 | Stationary stochastic processes |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
generalized hyperbolic; generalized inverse Gaussian; Ornstein-Uhlenbeck process; subordinator model; long range dependenceReferences:
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