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Asymptotic analysis of a double integral occurring in the rough Bergomi model. (English) Zbl 1454.41012

The author provides an asymptotic formula for the third moment of the log-price in the rough Bergomi model when the Hurst parameter approaches zero. The main tools are hypergeometric identities and uniform asymptotic formulas of incomplete gamma functions.

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
33C05 Classical hypergeometric functions, \({}_2F_1\)
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