Generalized hyperbolic diffusion processes with applications in finance. (English) Zbl 0980.91039

Summary: A special class of diffusion processes, the generalized hyperbolic diffusion processes, is introduced. As a byproduct we present a technique for the construction of one-dimensional ergodic diffusion processes with a predetermined stationary density. We specifically study the application of this new type of diffusion process to financial data, especially U.S. stock prices. It is seen that in addition to confirming stylized features of the financial market, a key explanation concerning “thick-”tailed log returns is provided.


91B28 Finance etc. (MSC2000)
60J60 Diffusion processes
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