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

Peregrine Securities, 2012

38 Pages Posted: 21 Apr 2016

See all articles by Emlyn James Flint

Emlyn James Flint

Legae Peresec; Department of Actuarial Science, University of Cape Town

Florence Chikurunhe

Peregrine Securities

Anthony Seymour

University of Cape Town (UCT)

Date Written: August 13, 2012

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.

Keywords: Nonparametric option price, Risk-neutral historical distributions, Canonical valuation

JEL Classification: C14, C15, C5, G13

Suggested Citation

Flint, Emlyn James and Chikurunhe, Florence and Seymour, Anthony, (Un)Modelling the Volatility Surface: Valuing South African Volatility Surfaces Via Risk-Neutral Historic Return Distributions (August 13, 2012). Peregrine Securities, 2012. Available at SSRN: https://ssrn.com/abstract=2767409 or http://dx.doi.org/10.2139/ssrn.2767409

Emlyn James Flint (Contact Author)

Legae Peresec ( email )

15 Cavendish Street
Claremont
Cape Town, Western Cape 7700
South Africa
27117227556 (Phone)

HOME PAGE: http://www.legaeperesec.co.za

Department of Actuarial Science, University of Cape Town ( email )

Actuarial Science Section, University of Cape Town
Private Bag X3, Rondebosch
Cape Town, Western Cape 7701
South Africa
+27 21 650 2475 (Phone)

Florence Chikurunhe

Peregrine Securities ( email )

21 Main Road
Claremont
Cape Town, Western Cape 7700
South Africa
+27117227551 (Phone)

HOME PAGE: http://www.peregrine.co.za

Anthony Seymour

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

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