Derivatives Pricing with Fractional Discrete-time Models

Jayaraman, Sarath Kumar

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