Model risk quantification in option pricing

Abstract: This thesis investigates a methodology for quantification of model risk in option pricing. A set of different pricing models is specified and each model is assigned a probability weight based on the Akaike Information Criteria. It is then possible to obtain a price distribution of an exotic derivative from these probability weights. Two measures of model risk inspired by the regulatory standards on prudent valuation are proposed based on this methodology. The model risk measures are studied for different equity options which are priced using a set of stochastic volatility models, with and without jumps. The models are calibrated to vanilla call options from the S&P 500 index, as well as to synthetic option prices based on market data simulated using the Bates model. For comparable options, the model risk is higher for up-and-out barrier options compared to vanilla, digital and Asian options. Moreover, the model risk measure, in relative terms of option price, increases quickly with strike level for call options far out of the money, while the model risk in absolute terms is lowest when the option is deep out of the money. The model risk for up-and-out barrier options tends to be higher when the barrier is closer to the spot price, although the increase in risk does not have to be monotonic with decreasing barrier level. The methodology is flexible and easy to implement, yielding intuitive results. However, it is sensitive to different assumptions in the structure of the pricing errors.