Local Volatility Modeling of JSE Exotic Can-Do Options

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