Dynamics of the implied volatility surface. Theory and empirical evidence

I perform a regression analysis to test two of the most famous heuristic rules existing in the literature concerning the behavior of the implied volatility surface. These rules are the <italic>sticky delta</italic> rule and the <italic>sticky strike</italic> rule. I present a new specification to test the sticky strike rule that allows for dynamics in the implied volatility surface. In the empirical application, I use monthly implied volatility surfaces corresponding to the IBEX 35 index. The estimation results show that the extended specification for the sticky strike rule presented in this article better represents the behavior of the implied volatility under this rule. Furthermore, there is not one rule that is the most appropriate at all times to explain the evolution of the implied volatility surface. Depending on the market situation, one rule may be more appropriate than another. In particular, when the underlying asset displays trend, the sticky delta rule tends to prevail against the sticky strike rule. Conversely, when the underlying asset moves in range, then the sticky strike rule tends to predominate.