Risk neutral measures and GARCH model calibration

Empirical studies have shown that GARCH models can be successfully used to describe option prices. Pricing such option contracts requires the risk neutral return dynamics of underlying asset. Since under the GARCH framework the market is incomplete, there is more than one risk neutral measure. In this thesis, we study the locally risk neutral valuation relationship, the mean correcting martingale measure, the conditional Esscher transform and the second order Esscher transform as martingale measure candidates. All these methods lead to the respective risk neutral return dynamics. We empirically examine in-sample and out-ofsample performance of Gaussian-TGARCH and Normal inverse Gaussian (NIG)-TGARCH models under these risk neutral measures.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor dc:publisher.institution

Graduate Studies

Year dc:date.issued

2012

Author dc:creator

• LI, SHENG

Advisor dc:contributor.advisor

• Badescu, Alexandru

• Mathematics

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

eng

DOI

http://dx.doi.org/10.11575/PRISM/27669

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:11023/221