Non-normalities in returns on the all ordinaries index : implicit Bayesian inference using option prices

Abstract

The Black-Scholes model is the most common tool for pricing options, with one of its main addumptions being that returns on the underlying asset follow a normal distributin. In practice, the bulk of the empirical evidence shows most financial returns to be characterised by non-normalities, a feature which, in turn, is associated with mispricing of the Black-Scholes model. In view of this evidence an option price model is developed which allows for skewness and kurtosis in the underlying returns processs. Using Bayesdian methodology, inference about the process is conducted implicitly using observed option priced, with posterior distributions estimated for the parameters of the alternative models. To discriminate between models a number of selection criteria are used, includingimplicit model probabilities, out-of-sample fit and predictive performance and implied volatility smiles. In addition, Bayesian model averaging is invoked to produce a predictive density which has been aversaged across all model-specific predictives. The methodology is applied to option prices on the All Ordinaries Stock Index. The results favour the skewed normal model although no one model clearly dominates. The option price model evaluates the payoff function of the option directly by specifying a distribution for the underlying return over the life of the option. Using this method one can apply standsrd, one-dimendional numerical quadrature procedures to the expectation needed to compute the option price and avoid the use og Monte Carlo methods. Not only is this approach considerably faster computationally but it is also shown to be more accurate.