Extrapolation analytics for dupire’s local volatility

Abstract

We consider wing asymptotics of local volatility surfaces. While our recent paper in the journal Risk (De Marco et al. Risk 2:82–87, 2013, [3]) discusses our approximation formula from a practical and numerical perspective, the present paper focuses on rigorous proofs of the approximations. We apply the saddle point method (Heston model) and Hankel contour integration (variance gamma model).