Arbitrage-free implied volatility surfaces for options on single stock futures

The current method employed by the Johannesburg Stock Exchange1 (JSE) to determine implied volatility is based on trade data and a linear deterministic approach. The aim of this paper is to construct a market-related arbitrage-free implied volatility surface, by using a quadratic deterministic function, for two stock indices and ten single stock futures (SSFs). Actual traded data is used and we show practically how all no-arbitrage conditions are implemented and tested.