Affine GARCH option pricing models, stochastic interest rates, and diffusion limits
| dc.contributor.advisor | Badescu, Alexandru | |
| dc.contributor.author | Gu, Zhouzhou | |
| dc.contributor.committeemember | Qiu, Jinniao | |
| dc.contributor.committeemember | Swishchuk, Anatoliy | |
| dc.date | 2022-11 | |
| dc.date.accessioned | 2022-09-20T16:03:19Z | |
| dc.date.available | 2022-09-20T16:03:19Z | |
| dc.date.issued | 2022-09 | |
| dc.description.abstract | This article proposes a derivative pricing framework when the asset returns and the short term rate process are modelled with affine GARCH models driven by correlated Gaussian innovations. The risk neutral dynamics are derived based on a co-variance dependent pricing kernel and semi-closed form solutions are derived for European style options and bond prices. We further derive the weak diffusion limits of the underlying processes under both physical and risk-neutral measure and we investigate the consistency between the proposed pricing kernel with the well-known Girsanov principle in continuoustime. A variety of numerical exercises are provided to analyze the validity of our pricing formulae, the sensitivity of the option prices relative to the pricing kernel parameters, and the convergence of option prices to those based on the limiting diffusions. Finally, we illustrate an empirical analysis based on a joint estimation using historical asset returns and short-term rates, and cross sections of options and bond prices. | en_US |
| dc.identifier.citation | Gu, Z. (2022). Affine GARCH option pricing models, stochastic interest rates, and diffusion limits (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1880/115245 | |
| dc.identifier.uri | https://dx.doi.org/10.11575/PRISM/40257 | |
| dc.language.iso | eng | en_US |
| dc.publisher.faculty | Science | en_US |
| dc.publisher.institution | University of Calgary | en |
| 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. | en_US |
| dc.subject | option pricing | en_US |
| dc.subject | affine models | en_US |
| dc.subject | stochastic interest rate | en_US |
| dc.subject | co-variance dependent pricing kernels | en_US |
| dc.subject | diffusion limits | en_US |
| dc.subject.classification | Education--Mathematics | en_US |
| dc.title | Affine GARCH option pricing models, stochastic interest rates, and diffusion limits | en_US |
| dc.type | master thesis | en_US |
| thesis.degree.discipline | Mathematics & Statistics | en_US |
| thesis.degree.grantor | University of Calgary | en_US |
| thesis.degree.name | Master of Science (MSc) | en_US |
| ucalgary.item.requestcopy | true | en_US |