Model Risk in Pricing and Hedging of Financial Derivatives

Specialeforsvar ved Jeppe Højgaard Krog

Titel: Model Risk in Pricing and Hedging of Financial Derivatives

Abstract: In this thesis, a framework to quantify model risk within option pricing is suggested and studied. Multiple models with different dynamics are presented, and from these a set of pricing models is generated. Each model is assigned a probability weight using the Bayesian Information Criterion giving rise to a weighted price distribution for some financial derivative. Two model risk measures are suggested with inspiration from the European Regulatory Technical Standards on additional value adjustments, the Federal Reserves supervisory letter on model risk, as well as the axiomatic framework established in Cont (2006). The models are calibrated to the volatility surface of the S&P 500 index. The model risk of vanilla, Asian, barrier and autocallable options across different days and market structures is studied. The model risk is shown to be dependent on the specific option features, and the Asian and barrier options are found to be relatively stable over time in terms of relative model risk, whereas the autocallable is more variable. Furthermore, a measure of an option's path-dependency is suggested and held up against the model risk measures. Finally, the stability of the framework is analyzed, and potential improvements are discussed. The framework is transparent, fairly easy to implement, and it provides intuitive results. However, it is subject to several limiting assumptions, such as the distributional assumption on the pricing errors, which is used when assigning the probability weights.

Vejleder: Rolf Poulsen
Censor: Thomas Kokholm