Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/178554
Authors: 
Kotzé, Antonie
Oosthuizen, Rudolf
Pindza, Edson
Year of Publication: 
2015
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 8 [Year:] 2015 [Issue:] 1 [Pages:] 43-82
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.
Subjects: 
exotic options
JSE
Can-Do options
implied volatility
local volatility
dupire transforms
gyöngy theorem
calibration
deterministic volatility function
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by/4.0/
Document Type: 
Article

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