A Note about Characterization of Calendar Spread Arbitrage in eSSVI Surfaces

This paper provides a little correction to a proposition about calendar spread arbitrage in eSSVI volatility surfaces and gives exact conditions under which two eSSVI slices have tangency points without crossing over each other. The original proposition was stated in the paper where Hendriks and Martini (2019) introduced the eSSVI surface model. However the original statement (and the one given in a preprint version which is slightly different) is wrong and from the original proofs (which are slightly different in the preprint and final article) it is not obvious to infer the correct statement. The proof given in this paper is based on the main ideas of the original proof, but it fills in several details which eventually lead to a sharper result.