Model risk for barrier options when priced under different lévy dynamics

Mbakwe, Chidinma (2011-12)

Thesis (MSc)--Stellenbosch University, 2011.

Thesis

ENGLISH ABSTRACT: Barrier options are options whose payoff depends on whether or not the underlying asset price hits a certain level - the barrier - during the life of the option. Closed-form solutions for the prices of these path-dependent options are available in the Black-Scholes framework. It is well{known, however, that the Black-Scholes model does not price even the so-called vanilla options correctly. There are a number of popular asset price models based 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 barrier options in several exponential Lévy models. First, the Variance Gamma, Normal Inverse Gaussian and CGMY models are calibrated to market-observed vanilla option prices. Barrier option prices are then evaluated in these models using Monte Carlo methods. The prices obtained are then compared to each other, as well as the Black-Scholes prices. It is observed that the different exponential Lévy models yield barrier option prices which are quite close to each other, though quite different from the Black-Scholes prices. This suggests that the associated model risk is low.

AFRIKAANSE OPSOMMING: Versperring opsies is opsies met 'n afbetaling wat afhanklik is daarvan of die onderliggende bateprys 'n bepaalde vlak - die versperring - bereik gedurende die lewe van die opsie, of nie. Formules vir die pryse van sulke opsies is beskikbaar binne die Black-Scholes raamwerk. Dit is egter welbekend dat die Black-Scholes model nie in staat is om selfs die sogenaamde vanilla opsies se pryse korrek te bepaal nie. Daar bestaan 'n aantal populêre bateprysmodelle gebaseer op eksponensiële Lévy-dinamika, wat almal in staat is om die mark-waarneembare vanilla opsie pryse te herproduseer. Hierdie tesis ondersoek die potensiële modelrisiko geassosieer met die prysbepaling van versperring opsies in verskeie eksponseniële Lévy-modelle. Eers word die Variance Gamma{, Normal Inverse Gaussian- en CGMY-modelle gekalibreer op mark-waarneembare vanilla opsiepryse. Die pryse van versperring opsies in hierdie modelle word dan bepaal deur middel van Monte Carlo metodes. Hierdie pryse word dan met mekaar vergelyk, asook met die Black-Scholespryse. Dit word waargeneem dat die versperring opsiepryse in die verskillende eksponensiële Lévymodelle redelik na aan mekaar is, maar redelik verskil van die Black-Scholespryse. Dit suggereer dat die geassosieerde modelrisiko laag is.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/17810
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