Derivatives Pricing with Fractional Discrete-time Models
| dc.contributor.advisor | Badescu, Alexandru | |
| dc.contributor.author | Jayaraman, Sarath Kumar | |
| dc.contributor.committeemember | Godin, Frederic | |
| dc.contributor.committeemember | Qiu, Jinniao | |
| dc.contributor.committeemember | Swishchuk, Anatoliy | |
| dc.contributor.committeemember | Ware, Antony | |
| dc.date | 2022-11 | |
| dc.date.accessioned | 2022-07-18T22:12:39Z | |
| dc.date.available | 2022-07-18T22:12:39Z | |
| dc.date.issued | 2022-07-07 | |
| dc.description.abstract | This thesis studies the pricing of European style derivatives with various affine models. Most of this thesis focuses on the impact of long memory on asset return modelling and option pricing. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH(∞) representations. It not only nests a large variety of option pricing models from the literature, but also allows for the introduction of novel fractionally integrated processes for option valuation purposes. Using an infinite sum characterization of the log-asset price’s cumulant generating function, we derive semi-explicit expressions for European option prices under a variance-dependent stochastic discount factor. We carry out an extensive empirical analysis which includes estimations based on different combinations of returns and options of the S&P 500 index for a variety of short- and long-memory models. Our results indicate that the inclusion of long memory into return modelling substantially improves the option pricing performance. Using a set of out-of-sample option pricing errors, we show that long-memory models outperform richer parametrized one- and two-component models with short-memory dynamics. The last part of the thesis studies the pricing of volatility derivatives with affine models. We propose semi-closed form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options. | en_US |
| dc.identifier.citation | Jayaraman, S. K. (2022). Derivatives pricing with fractional discrete-time models (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/39916 | |
| dc.identifier.uri | http://hdl.handle.net/1880/114854 | |
| 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 | Fractional GARCH | en_US |
| dc.subject | Affine models | en_US |
| dc.subject | Variance-dependent pricing kernels | en_US |
| dc.subject | Long memory | en_US |
| dc.subject | VIX options | en_US |
| dc.subject | Target volatility options | en_US |
| dc.subject | Heston-Nandi GARCH | en_US |
| dc.subject | Inverse Gaussian GARCH | en_US |
| dc.subject.classification | Education--Finance | en_US |
| dc.subject.classification | Education--Mathematics | en_US |
| dc.subject.classification | Economics | en_US |
| dc.subject.classification | Statistics | en_US |
| dc.title | Derivatives Pricing with Fractional Discrete-time Models | en_US |
| dc.type | doctoral thesis | en_US |
| thesis.degree.discipline | Mathematics & Statistics | en_US |
| thesis.degree.grantor | University of Calgary | en_US |
| thesis.degree.name | Doctor of Philosophy (PhD) | en_US |
| ucalgary.item.requestcopy | true | en_US |