Moment generating functions and Normalized implied volatilities: unification and extension via Fukasawa's pricing formula

Stefano De Marco, Claude Martini

We extend the model-free formula of [Fukasawa 2012] for $\mathbb{E}[\Psi (X_T)]$, where $X_T=\log S_T/F$ is the log-price of an asset, to functions $\Psi$ of exponential growth. The result…