Thesis (MSc)--Stellenbosch University, 2011. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/17810 |
| Date | 12 1900 |
| Creators | Mbakwe, Chidinma |
| Contributors | Ouwehand, Peter, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 104 p. : ill. |
| Rights | Stellenbosch University |
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