Testing Extended Rules of Thumb for the Dynamics of Volatility Surfaces

Abstract: It is a common practise to quote option prices using their BlackScholes implied volatility. A volatility surface describes an options implied volatility as a function of the strike price and time to maturity. It can be used as a tool for hedging but also valuation when prices are not directly observable. The short-term evolution of this surface has been described by a variety of apocryphal rules. Three of these rules are tested empirically for exchange traded S&P 500 index options for two distinguished periods. The square root of time rule, consistent with the no-arbitrage condition, has the highest explanatory and predictive power. Extended versions are also derived but with no significant improvement.