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

TL;DR

This paper establishes exact mathematical relationships linking the ATM implied volatility slope, volatility swaps, and zero vanna implied volatility, enhancing understanding of their interconnected dynamics in options markets.

Contribution

It provides precise formulas connecting key implied volatility measures and derivatives, offering new insights into their relationships.

Findings

Derived exact relationships between implied volatility slope and volatility swaps.

Linked zero vanna implied volatility with other volatility measures.

Enhanced theoretical understanding of volatility surface dynamics.

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.