Model risk for barrier options when priced under different lévy dynamics

[摘要] ENGLISH ABSTRACT: Barrier options are options whose payoffdepends on whether or not the underlying assetprice hits a certain level - the barrier - during the life of the option. Closed-form solutionsfor the prices of these path-dependent options are available in the Black-Scholesframework. It is well{known, however, that the Black-Scholes model does not price eventhe so-called vanilla options correctly. There are a number of popular asset price modelsbased on exponential Lévy dynamics which are all able to capture the volatility smile, i.e.reproduce market-observed prices of vanilla options.This thesis investigates the potential model risk associated with the pricing of barrieroptions in several exponential Lévy models. First, the Variance Gamma, Normal InverseGaussian and CGMY models are calibrated to market-observed vanilla option prices. Barrieroption prices are then evaluated in these models using Monte Carlo methods. Theprices obtained are then compared to each other, as well as the Black-Scholes prices. Itis observed that the different exponential Lévy models yield barrier option prices whichare quite close to each other, though quite different from the Black-Scholes prices. Thissuggests that the associated model risk is low.

[发布机构] Stellenbosch University