Thesis (MSc)--Stellenbosch University, 2015 / AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling
in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in
verband met die prysbepaling van vanielje-en eksotiese opsies, en vergelyk die prestasie
van verskeie Lévy modelle. ’n Nuwe metode om modelrisiko te meet word ook voorgestel
(hoofstuk 6). Ons kalibreer eers verskeie Lévy modelle aan die log-opbrengs van die
S&P500 indeks. Statistiese toetse en grafieke voorstellings toon albei aan dat suiwer
sprongmodelle (VG, NIG en CGMY) die verdeling van die opbrengs beter beskryf as
die Black-Scholes model. Daarna kalibreer ons hierdie vier modelle aan S&P500 indeks
opsie data en ook aan "CGMY-wˆ ereld" data (’n gesimuleerde wÃłreld wat beskryf word
deur die CGMY-model) met behulp van die wortel van gemiddelde kwadraat fout. Die
CGMY model vaar beter as die VG, NIG en Black-Scholes modelle. Ons waarneem
ook ’n effense verskil tussen die nuwe parameters van CGMY model en sy wisselende
parameters, ten spyte van die feit dat CGMY model gekalibreer is aan die "CGMYwêreld"
data. Versperrings-en terugblik opsies word daarna geprys, deur gebruik te
maak van die gekalibreerde parameters vir ons modelle. Hierdie pryse word dan vergelyk
met die "ware" pryse (bereken met die ware parameters van die "CGMY-wêreld), en
’n beduidende verskil tussen die modelpryse en die "ware" pryse word waargeneem.
Ons eindig met ’n poging om hierdie modelrisiko te kwantiseer / ENGLISH ABSTRACT : The growing interest in calibration and model risk is a fairly recent development in
financial mathematics. This thesis focussing on these issues, particularly in relation to
the pricing of vanilla and exotic options, and compare the performance of various Lévy
models. A new method to measure model risk is also proposed (Chapter 6). We calibrate
only several Lévy models to the log-return of S&P500 index data. Statistical tests
and graphs representations both show that pure jump models (VG, NIG and CGMY) the
distribution of the proceeds better described as the Black-Scholes model. Then we calibrate
these four models to the S&P500 index option data and also to "CGMY-world" data
(a simulated world described by the CGMY model) using the root mean square error.
Which CGMY model outperform VG, NIG and Black-Scholes models. We observe also a
slight difference between the new parameters of CGMY model and its varying parameters,
despite the fact that CGMY model is calibrated to the "CGMY-world" data. Barriers
and lookback options are then priced, making use of the calibrated parameters for our
models. These prices are then compared with the "real" prices (calculated with the true
parameters of the "CGMY world), and a significant difference between the model prices
and the "real" rates are observed. We end with an attempt to quantization this model
risk.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/98030 |
| Date | 12 1900 |
| Creators | Mboussa Anga, Gael |
| Contributors | Ouwehand, Peter, Stellenbosch University. Faculty of Science. Department Mathematical Sciences (Mathematicas) |
| Publisher | Stellenbosch : Stellenbosch University, Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
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