publication . Preprint . Article . 2017

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

Stefano De Marco; Claude Martini;
Open Access English
  • Published: 02 Mar 2017
Abstract
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 resulting integral representation is written in terms of normalized implied volatilities. Just as Fukasawa's work provides rigourous ground for Chriss and Morokoff's (1999) model-free formula for the log-contract (related to the Variance swap implied variance), we prove an expression for the moment generating function $\mathbb E[e^{p X_T}]$ on its analyticity domain, that encompasses (and extends) Matytsin's formula [Matytsin 2000] for the characteristic function $\mathbb E[e^{i \eta X...
Subjects
free text keywords: Quantitative Finance - Pricing of Securities, Normalization (statistics), Variance swap, Moment-generating function, Financial economics, Characteristic function (probability theory), Implied volatility, Unification, Mathematics, Integral representation, Duality (optimization)

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