Arbitrage-Free Implied Volatility Surfaces for Options on Single Stock Futures

Posted: 10 Jan 2013

See all articles by Antonie Kotze

Antonie Kotze

Financial Chaos Theory; Department of Finance and Investment Management

Coenraad Labuschagne

University of the Witwatersrand

Merrell Nair

ABSA Capital Bank

Nadine Padayachi

University of the Witwatersrand

Date Written: December 11, 2012

Abstract

The current method employed by the Johannesburg Stock Exchange (JSE) to determine implied volatility is based on trade data and a linear deterministic approach. The aim of this paper is to construct a market-related arbitrage-free implied volatility surface, by using a quadratic deterministic function, for two stock indices and ten single stock futures (SSFs). Actual traded data is used and we show practically how all no-arbitrage conditions are implemented and tested.

Keywords: Volatility surface, options on single stock futures, quadratic deterministic function

JEL Classification: C61, G17

Suggested Citation

Kotze, Antonie and Labuschagne, Coenraad and Nair, Merrell and Padayachi, Nadine, Arbitrage-Free Implied Volatility Surfaces for Options on Single Stock Futures (December 11, 2012). North American Journal of Economics and Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2198351

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

Coenraad Labuschagne

University of the Witwatersrand ( email )

1 Jan Smuts Avenue
Johannesburg, Gauteng 2000
South Africa

Merrell Nair

ABSA Capital Bank ( email )

15 Alice Lane
Sandton, 2196
South Africa

Nadine Padayachi

University of the Witwatersrand ( email )

1 Jan Smuts Avenue
Johannesburg, Gauteng 2000
South Africa

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