# The ATM implied volatility slope, the (dual) volatility swap, and the (dual) zero vanna implied volatility

**Authors:** Frido Rolloos  
**arXiv:** [2202.07542](https://arxiv.org/abs/2202.07542)  
**Date:** 2022-02-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2202.07542v1/

## Abstract

Exact relationships between the short time-to-maturity ATM implied volatility slope, the (dual) volatility swap, and the (dual) zero vanna implied volatility are given.