The implied volatility of Forward-Start options: ATM short-time level, skew and curvature

TL;DR

This paper derives explicit formulas for the at-the-money implied volatility, skew, and curvature of forward-start options in Markovian stochastic volatility models using Malliavin Calculus.

Contribution

It provides new closed-form expressions for forward implied volatility features in continuous-path stochastic volatility models.

Findings

Explicit formulas for ATM implied volatility, skew, and curvature.

Applicable to general Markovian stochastic volatility models.

Enhances understanding of forward-start option pricing.

Abstract

Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.