(Un)Modelling the Volatility Surface: Valuing South African Volatility Surfaces Via Risk-Neutral Historic Return Distributions

Abstract

The Black-Scholes framework implies a constant volatility across term and strike, and a lognormal distribution for underlying asset prices. However, it is known that empirical data violates this assumption. In this report we describe, motivate and apply a model-independent, historically-consistent method for estimating the ‘fair' volatility surface of an asset, which does not impose restrictive – and often incorrect – market assumptions. In so doing, we provide market participants with the following: (1) Important information on South African (SA) index return statistics and highlight what characteristics investors should be concerned with; (2) A review of historic SA index volatility skews and term structure, their evolutions over time and the current volatility scenario; (3) A tractable and customisable tool for investors and managers giving access to rich/cheap indicators across both strike and term for assets with existing volatility skews. These indicators are easily assimilated into existing measures such as the 90/110 skew spread and the realised-implied spread; (4) A statistically rigorous and standardised method to calculate comprehensive ‘fair' volatility skews for illiquid assets such as single stocks and bespoke basket indices; and (5) A simple method of incorporating investor's market views within the framework to calculate ‘fair' volatility skews that are consistent with future expectations.