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

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.