Venturing into Uncharted Territory: An Extensible Parametric Implied Volatility Surface Model

66 Pages Posted: 19 Jul 2021 Last revised: 15 Feb 2022

See all articles by Pascal Francois

Pascal Francois

HEC Montreal - Department of Finance

Rémi Galarneau-Vincent

HEC Montréal, Students

Geneviève Gauthier

Department of decision Sciences and GERAD; Associate member, Oxford-Man Institute (OMI)

Frédéric Godin

Concordia University, Quebec - Department of Mathematics & Statistics

Date Written: February 14, 2022

Abstract

A new parametric representation of implied volatility surfaces is proposed. The factors adequately capture the moneyness and maturity slopes, the smile attenuation, and the smirk. Furthermore, the implied volatility specification is twice continuously differentiable and well behaved asymptotically, allowing for clean interpolation and extrapolation over a wide range of moneyness and maturity. Fitting performance on S&P 500 options compares favourably with existing benchmarks. The benefits of a smoothed implied volatility surface are illustrated through the valuation of illiquid index derivatives, the extraction of the risk-neutral density and risk-neutral moments, the calculation of option price sensitivities, and the calculation of SVIX for the equity risk premium lower bound.

Keywords: Implied volatility surfaces, Incomplete Markets, Derivatives pricing, Factor models.

Suggested Citation

Francois, Pascal and Galarneau-Vincent, Rémi and Gauthier, Genevieve and Godin, Frédéric, Venturing into Uncharted Territory: An Extensible Parametric Implied Volatility Surface Model (February 14, 2022). Available at SSRN: https://ssrn.com/abstract=3888243 or http://dx.doi.org/10.2139/ssrn.3888243

Pascal Francois

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada
514-340-7743 (Phone)
514-340-5632 (Fax)

Rémi Galarneau-Vincent

HEC Montréal, Students ( email )

Montreal
Canada

Genevieve Gauthier (Contact Author)

Department of decision Sciences and GERAD ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

Associate member, Oxford-Man Institute (OMI) ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Frédéric Godin

Concordia University, Quebec - Department of Mathematics & Statistics ( email )

1455 De Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

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