From volatility smiles to the volatility of volatility

Bernard Dumas () and Elisa Luciano

Decisions in Economics and Finance, 2019, vol. 42, issue 2, No 4, 387-406

Abstract: 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.

Keywords: Stochastic volatility; Implicit volatility; Forward volatility; VIX (search for similar items in EconPapers)
JEL-codes: G13 G17 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10203-019-00263-w

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