Forward start volatility swaps in rough volatility models

TL;DR

This paper investigates the pricing relationship of forward start volatility swaps and options within rough volatility models, highlighting how approximation errors depend on model parameters and time intervals.

Contribution

It establishes a theoretical link between forward start volatility swap prices and implied volatilities in rough volatility models, emphasizing the role of the Hurst parameter and time-to-maturity.

Findings

Approximation error depends only on the difference between maturity and forward start date.

Error in the correlated case with H in (0, 1/2) is independent of time to forward start.

Theoretical results apply in the short time-to-maturity limit.

Abstract

This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit the approximation error in the leading term of the correlated case with $H\in(0,\frac12)$ does not depend on the time to forward start date, but only on the difference between the maturity date and forward start date and on the Hurst parameter $H$.