Volatility: Expectations and Realizations

Embedded in option prices are market expectations regarding future volatility. While the assumption of rational expectations has been a popular paradigm, it is difficult to ignore the subjective nature of expectations. The objective of this paper is to make market expectations visible as they evolve over time, and to price options in line with prevailing expectations, be they rational or non-rational. We put forward an analytically convenient option pricing framework that accommodates both stochastic volatility and asymmetric volatility. Daily estimates of the implied pdf of volatility are obtained by estimating the option pricing model one day at a time. We do not impose too much structure on how expectations are updated over time, but allow market expectations to take their course.