The paper reviews models of the option surface and reduced-form models for stochastic volatility in continuous time, under the risk-neutral measure. It defines “forward volatilities,” analogous to forward interest rates in the theory of the term structure, and provides a proof that the forward volatility is a conditional expected value, under the risk-neutral measure, of the future spot volatility. The theory developed here is the analog of Heath–Jarrow–Morton bond-pricing theory. The link is established between forward volatilities and so-called “model-free” volatility measures such as the VIX.

From volatility smiles to the volatility of volatility

Dumas B.;Luciano E.
2019

Abstract

The paper reviews models of the option surface and reduced-form models for stochastic volatility in continuous time, under the risk-neutral measure. It defines “forward volatilities,” analogous to forward interest rates in the theory of the term structure, and provides a proof that the forward volatility is a conditional expected value, under the risk-neutral measure, of the future spot volatility. The theory developed here is the analog of Heath–Jarrow–Morton bond-pricing theory. The link is established between forward volatilities and so-called “model-free” volatility measures such as the VIX.
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http://springerlink.metapress.com/app/home/journal.asp?wasp=e0ggqgqvlk6e7r03eua0&referrer=parent&backto=linkingpublicationresults,1:100169,1
Forward volatility; Implicit volatility; Stochastic volatility; VIX
Dumas B.; Luciano E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1728915
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