Local Volatility Modeling of JSE Exotic Can-Do Options

47 Pages Posted: 1 Apr 2015

See all articles by Antonie Kotze

Antonie Kotze

Financial Chaos Theory; Department of Finance and Investment Management

Rudolf Oosthuizen

JSE Securities Exchange

Edson Pindza

University of Pretoria

Multiple version iconThere are 2 versions of this paper

Date Written: December 8, 2014

Abstract

Can-Do Options are derivative products listed on the JSE's derivative exchanges -- mostly equity derivative products listed on Safex and currency derivative products listed on Yield-X. These products give investors the advantages of listed derivatives with the flexibility of over the counter (OTC) contracts. Investors can negotiate the terms for all option contracts, choosing the type of option, underlying asset and the expiry date. Many exotic options and even exotic option structures are listed. Exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Most exotic options on Safex and Yield-X are valued by local volatility models. 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 the volatility to be constant.

In this document we discuss various topics that in influence the successful construction of implied and local volatility surfaces in practice. We focus on arbitrage-free conditions, choice of calibrating functionals and selection of numerical algorithms to price options. We illustrate our methodologies by studying the local volatility surfaces of South African index and foreign exchange options. Numerical experiments are conducted using Excel and MATLAB.

Keywords: Exotic options, JSE, Can-Do Options, Implied Volatility, Local Volatility, Dupire Transforms, Gyongy Theorem, Markov Projection

JEL Classification: C61, G13, G17

Suggested Citation

Kotze, Antonie and Oosthuizen, Rudolf and Pindza, Edson, Local Volatility Modeling of JSE Exotic Can-Do Options (December 8, 2014). Available at SSRN: https://ssrn.com/abstract=2587376 or http://dx.doi.org/10.2139/ssrn.2587376

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

Rudolf Oosthuizen

JSE Securities Exchange ( email )

United States

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

Edson Pindza

University of Pretoria

Physical Address Economic and Management Sciences
Pretoria, Gauteng 0002
South Africa

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