Predicting the smile: A study on the properties of the volatility surface of S&P Composite 500 Index option

Abstract: The classic Black-Scholes model on option pricing from 1973 has been a widely debated and scrutinized theory over the past decades. Despite its proved limitations and simplifications, it remains as the most used pricing model of public traded options today. One implication of the model is the implied volatility surface, an empirical anomaly which has emerged over the past 25 years from the volatility of the underlying instrument. In this thesis, our goal is to create a parameterization of the daily volatility smiles of the S&P 500 Index option, and study the time-series properties of these parameters. We do this by testing the explanatory power of exogenous variables, and by using different lag models to predict the shape of the smile. Our results indicate strong correlations with our external factors, but a non-conclusive predictive power of the inherent parameters. The forecasting properties of the smile seem to remain a mystery.