Modelling South African single-stock futures option volatility smiles

Abstract

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.