Constructing a South African Index Volatility Surface from Exchange Traded Data

37 Pages Posted: 10 Jan 2013

See all articles by Antonie Kotze

Antonie Kotze

Financial Chaos Theory; Department of Finance and Investment Management

Angelo Joseph

University of South Africa - School of Business Leadership

Date Written: November 10, 2009

Abstract

The exchange traded index option market in South Africa has seen tremendous growth during the last couple of years. The biggest liquidity is in options on the near and middle Alsi future contracts. Alsi futures are listed future contracts on the FTSE/JSE Top40 index, the most important and tradable equity index in South Africa. OTC and listed options trade on a skew and most market makers have implemented their own proprietary skew generators. Clearing houses also use the volatility surface in estimating the initial margins for options.

In this paper we show how to generate the implied volatility surface by fitting a quadratic deterministic function to implied volatility data from Alsi index options traded on Safex. This market is mostly driven by structured spread trades, and very few at-the-money options ever trade. It is thus difficult to obtain the correct at-the-money volatilities needed by the exchange for their mark-to-market and risk management processes. We further investigate the term structure of at-the-money volatilities and show how the at-the-money implied volatilities can be obtained from the same deterministic model. This methodology leads to a no-spread arbitrage and robust market related volatility surface that can be used by option traders and brokers in pricing structured option trades.

Keywords: Volatility, volatility skew, volatility surface, smile, Alsi, JSE, index, quadratic deterministic function

JEL Classification: C61, G17

Suggested Citation

Kotze, Antonie and Joseph, Angelo, Constructing a South African Index Volatility Surface from Exchange Traded Data (November 10, 2009). Available at SSRN: https://ssrn.com/abstract=2198357 or http://dx.doi.org/10.2139/ssrn.2198357

Antonie Kotze (Contact Author)

Financial Chaos Theory ( email )

PO Box 16185
Doornfontein, 2028
South Africa

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

Department of Finance and Investment Management ( email )

PO Box 524
Auckland Park
Johannesburg, Gauteng 2006
South Africa

HOME PAGE: http://www.uj.ac.za

Angelo Joseph

University of South Africa - School of Business Leadership ( email )

P.O. Box 392
UNISA
Pretoria, Gauteng 0003
South Africa

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