Generalized arbitrage-free SVI volatility surfaces

Abstract

In this paper we propose a generalization of the recent work by Gatheral and Jacquier [J. Gatheral and A. Jacquier, Quant. Finance, 14 (2014), pp. 59-71] on explicit arbitrage-free parameterizations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper [M. Roper, Arbitrage-Free Implied Volatility Surfaces, preprint, School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales, Australia, 2010, http://www.maths.usyd.edu.au/u/pubs/publist/preprints/ 2010/roper-9.pdf]. We further exhibit an arbitrage-free volatility surface different from Gatheral's SVI parameterization.