Stock index futures markets: stochastic volatility models and smiles

This study examined whether the inclusion of an appropriate stochastic volatility that captures key distributional and volatility facets of stock index futures is sufficient to explain implied volatility smiles for options on these markets. I considered two variants of stochastic volatility models related to Heston (1993). These models are differentiated by alternative normal or nonnormal processes driving log‐price increments. For four stock index futures markets examined, models including a negatively correlated stochastic volatility process with nonnormal price innovations performed best within the total sample period and for subperiods. Using these optimal stochastic volatility models, I determined the prices of European options. When comparing simulated and actual options prices for these markets, I found substantial differences. This suggests that the inclusion of a stochastic volatility process consistent with the objective process alone is insufficient to explain the existence of smiles. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:43–78, 2001