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What Does Today’s Smile Imply About Future Volatilities?

Riccardo Rebonato
The Journal of Derivatives Spring 2020, jod.2019.1.091; DOI: https://doi.org/10.3905/jod.2019.1.091
Riccardo Rebonato
is a professor at the EDHEC Risk Institute of the EDHEC Business School in London, UK
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Abstract

This article presents a simple and financially justifiable way to extract the evolution of the smile surface in the (ℚ) measure from today’s plain vanilla option prices. By combining this information with (ℙ)-measure estimation of the dependence of implied volatility on the underlying, one can 1) obtain information about the existence and magnitude of a volatility risk premium; 2) devise trading strategies; and 3) price options such as Forward Volatility Agreements (FVAs).

TOPICS: Options, analysis of individual factors/risk premia, factor-based models, style investing

Key Findings

  • • Plain vanilla smiles of different maturities are compatible with an infinity of future smiles, but these are linked by strong consistency relationships, which we identify.

  • • Using these consistency relationships and very mild assumptions, we obtain the future smiles that are most compatible with space and time homogeneity and price today’s plain-vanilla options.

  • • There is an interesting discrepancy between the dependence of ATM volatilities in the future smiles so obtained and the empirical dependence of the same quantity.

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The Journal of Derivatives: 28 (2)
The Journal of Derivatives
Vol. 28, Issue 2
Winter 2020
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What Does Today’s Smile Imply About Future Volatilities?
Riccardo Rebonato
The Journal of Derivatives Nov 2019, jod.2019.1.091; DOI: 10.3905/jod.2019.1.091

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What Does Today’s Smile Imply About Future Volatilities?
Riccardo Rebonato
The Journal of Derivatives Nov 2019, jod.2019.1.091; DOI: 10.3905/jod.2019.1.091
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    • Abstract
    • STATEMENT OF THE PROBLEM
    • THE SPACE- AND TIME-HOMOGENEOUS CASE
    • THE PROCEDURE
    • WHAT DOES OUR APPROACH IMPLY ABOUT THE UNDERLYING PROCESS?
    • RESULTS
    • DISCUSSION OF THE RESULTS
    • TRADING STRATEGIES TO EXPLOIT PERCEIVED DISCREPANCIES
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