Tail Risk, Almost Stochastic Dominance and Index Option Anomalies

We use a novel definition of tail risk for option pricing purposes, based on the concept of almost stochastic dominance (ASD) in order to examine empirical “puzzles” documented in several high profile studies of the market for S&P 500 index options. We find that with one exception these studies have used a frictionless theoretical framework and modified the observed data to make it fit into it. Thus, they have ignored persistent features of the index option market data such as the wide bid-ask spreads for OTM options, the partial segmentation of the market for puts and calls, and the inconsistency of the results for different maturity options, which we document in our data. We concentrate on the claims that out-of-the money (OTM) put options and at-the-money (ATM) straddles are overpriced. We present simple theoretical models based on ASD of the end user option trader that incorporate these features and are parsimonious in terms of other assumptions. The empirical study makes use of new methods of inference for almost stochastic dominance. It finds that these puzzles disappear under such conditions and concludes that these apparent anomalies are probably due to the omission of the above features