Option Surface Econometrics with Applications

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution with expected values given by the option pricing model. The resulting setup allows for maximum likelihood estimation of option pricing model parameters with standard errors enabling the test of hypotheses. Hypothesis testing is illustrated by testing for risk neutral return distributions being consistent with Brownian motion with drift time changed by a subordinator. Models mixing processes of independent increments with processes related to solution of Ornstein Uhlenbeck (OU) equations are tested for the presence of the OU component. OU equations are a form of perpetual motion processes continuously responding to their past changes. The tests support the rejection of Brownian subordination and the presence of a perpetual motion component.