Empirical assessment and model selection in option pricing

Abstract

The majority of empirical option pricing studies consider the distance from the market option prices as the performance metric. Though, this kind of assessment is limited to the objectives of proper hedging of options and fair pricing of OTC contracts. Options can also be used in market e ciency tests. E ciency tests require positions in options and other assets (e.g. underlying security) with the objective to yield riskadjusted pro ts. If a model can generate excess pro t consistently, then it might claim that markets are not e cient. This study consists of four main parts. Di erent empirical option pricing studies are investigated in terms of assessment methodology. It is shown that error aggregation with data mining algorithms is a more robust way to assess model performance of a model. New model error metrics based on e ciency tests are introduced. Finally, all the new ndings are used in the introduction of a model selection framework. Model selection uses the price and hedge estimates of individual pricing models (e.g. Black-Scholes) to come up with better price and hedge structure according to the performance metric. Main motivation is to avoid over tting of complex models, by switching between simpler but e ective models according to performance shifts. Experiments with SPX and NDX contracts between 2009 and 2013 indicate that a model selection method with only a data mining algorithm to group errors and a simple selection rule, yields consistently better results than the individual models it uses.