Asymptotic analysis of a double integral occurring in the rough Bergomi model

Abstract

Recently, Forde et al. [The Rough Bergomi model as $H\to0$ -- skew flattening/blow up and non-Gaussian rough volatility; preprint] found an explicit expression for the third moment of the log-price in the rough Bergomi model, in terms of a double integral, whose integrand involves a hypergeometric function. One of the parameters of this financial market model, the Hurst parameter~$H$, is observed to be small in practice. We analyse the third moment asymptotically as $H$ tends to zero, using as our main tools hypergeometric transformation formulas and uniform asymptotic expansions for the incomplete gamma function.