Closed Form Pricing of European Options for a Family of Normal-Inverse Gaussian Processes

Abstract

In this article, the author assumes that the stock price dynamics follows the exponential of the normal-inverse Gaussian process. Analytical formulas for values of digital options and European calls are obtained. The considered family of the four-parametric normal-inverse Gaussian processes has steepness parameter . The established formulas depend on the values of the degenerate Appell hypergeometric function.

Keywords:

• Appell hypergeometric function
• Digital options
• Esscher measure
• European call and put
• Normal-inverse Gaussian process

Mathematics Subject Classification:

• Primary 60G51, 60-08
• Secondary 60K30, 33C20

ACKNOWLEDGMENTS

I am grateful to professor Albert N. Shiryaev for valuable discussions. I thank Professor K. Ano for important remarks. I am grateful to the unknown referee for precise reading of the article and the corrections that have improved it.