Constructing a South African Index Volatility Surface from Exchange Traded Data

Kotze, Antonie; Joseph, Angelo

doi:10.2139/ssrn.2198357

Cited by 11 publications

(9 citation statements)

References 27 publications

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“…We assume that trades with fewer than 15 days to maturity may have unreliable volatilities associated with closeout, and that the more reliable contract at that point would be the next available. This assumption is based on liquidity and parameter t-statistics and is confirmed in Kotze and Joseph (2009). This implies that, although we are analysing the "same" type of contract through time, we are experiencing a roll-over effect every 90 days in both the underlying index futures price and the option contract.…”

Section: Datamentioning

confidence: 64%

“…In an allied piece of research to ours, Kotze and Joseph (2009) give a detailed and clear explanation of the reasons for choosing to fit a deterministic quadratic function to this sort of data. Their work also specifies the various difficulties encountered with this process.…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…Of those conducted, de Araujo and Mare (2006) examined the volatility skew using risk-neutral historical distributions and Bonney, Shannon, and Uys (2008) did a principle component analysis of the Top40 volatility skew. Kotze and Joseph (2009) generated an implied volatility surface by fitting a quadratic deterministic function to data from ALSI index options. South African or international studies on the volatility surfaces of singlestock (futures) options are rare.…”

Section: Introductionmentioning

confidence: 99%

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Modelling South African single-stock futures option volatility smiles

Taylor¹

2014

Investment Analysts Journal

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The process of producing an implied volatility surface in the absence of reliable and frequent trade data is difficult. Bakshi, Kapadia and Madan (2003) detail a methodology for relating an index option smile structure with that of one of its constituents. Here we exploit this work to derive the single-stock option smile as a function of the index smile and a regressed relationship between the two underlying assets. Our non-parametric approach allows the market to estimate where implied volatilities should trade for illiquid derivative contracts away from at-the-money. The derived smile does not admit spread arbitrage.

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Section: Datamentioning

confidence: 64%

Section: Estimation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling South African single-stock futures option volatility smiles

Taylor¹

2014

Investment Analysts Journal

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“…To ensure the positivity of the numerator, we note that no-arbitrage arguments state that calendar spreads should have positive values. Kotzé and Joseph [44] and Kotzé et al [18] discusses no-arbitrage arguments in detail. We can turn these statements around: An implied volatility surface is arbitrage free if the local volatility is a positive real number (not imaginary) where σ loc (K, T ) ∈ R + 0 .…”

Section: Dupire Local Volatilitymentioning

confidence: 99%

“…Safex chose the first way for the liquid ALSI options and uses the following Three-parameter deterministic quadratic function as a good model of fit for the ALSI implied volatility data on every expiry date (for a full discussion see [18,44])…”

Section: The Deterministic Implied Volatility Functionmentioning

confidence: 99%

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

Kotze

Oosthuizen²,

Pindza

2015

JRFM

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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.

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