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Implied and Local Volatility Surfaces for South African Index and Foreign Exchange Options

Author

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  • Antonie Kotzé

    (Department of Finance and Investment Management, University of Johannesburg, PO Box 524, Aucklandpark 2006, South Africa)

  • Rudolf Oosthuizen

    (The Johannesburg Stock Exchange (JSE), One Exchange Square, Gwen Lane, Sandown 2196, South Africa)

  • Edson Pindza

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa)

Abstract

Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are proposed in order to overcome the shortcomings of the Black-Scholes model that assumes a constant volatility. The Johannesburg Stock Exchange (JSE) lists exotic options on its Can-Do platform. Most exotic options listed on the JSE’s derivative exchanges are valued by local volatility models. These models needs a local volatility surface. Dupire derived a mapping from implied volatilities to local volatilities. The JSE uses this mapping in generating the relevant local volatility surfaces and further uses Monte Carlo and Finite Difference methods when pricing exotic options. In this document we discuss various practical issues that influence the successful construction of implied and local volatility surfaces such that pricing engines can be implemented successfully. We focus on arbitrage-free conditions and the choice of calibrating functionals. We illustrate our methodologies by studying the implied and local volatility surfaces of South African equity index and foreign exchange options.

Suggested Citation

  • Antonie Kotzé & Rudolf Oosthuizen & Edson Pindza, 2015. "Implied and Local Volatility Surfaces for South African Index and Foreign Exchange Options," JRFM, MDPI, vol. 8(1), pages 1-40, January.
    • Handle: RePEc:gam:jjrfmx:v:8:y:2015:i:1:p:43-82:d:45139
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    References listed on IDEAS

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    Cited by:

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    2. Xin Yang & Shigang Wen & Zhifeng Liu & Cai Li & Chuangxia Huang, 2019. "Dynamic Properties of Foreign Exchange Complex Network," Mathematics, MDPI, vol. 7(9), pages 1-19, September.

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