A study of the Hobson and Rogers volatility model

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dc.contributor.advisor Carroll, Thomas en
dc.contributor.author Ryan, Gearóid
dc.date.accessioned 2015-11-05T12:23:01Z
dc.date.available 2015-11-05T12:23:01Z
dc.date.issued 2014
dc.date.submitted 2014
dc.identifier.citation Ryan, G. 2014. A study of the Hobson and Rogers volatility model. PhD Thesis, University College Cork. en
dc.identifier.uri http://hdl.handle.net/10468/2036
dc.description.abstract We firstly examine the model of Hobson and Rogers for the volatility of a financial asset such as a stock or share. The main feature of this model is the specification of volatility in terms of past price returns. The volatility process and the underlying price process share the same source of randomness and so the model is said to be complete. Complete models are advantageous as they allow a unique, preference independent price for options on the underlying price process. One of the main objectives of the model is to reproduce the `smiles' and `skews' seen in the market implied volatilities and this model produces the desired effect. In the first main piece of work we numerically calibrate the model of Hobson and Rogers for comparison with existing literature. We also develop parameter estimation methods based on the calibration of a GARCH model. We examine alternative specifications of the volatility and show an improvement of model fit to market data based on these specifications. We also show how to process market data in order to take account of inter-day movements in the volatility surface. In the second piece of work, we extend the Hobson and Rogers model in a way that better reflects market structure. We extend the model to take into account both first and second order effects. We derive and numerically solve the pde which describes the price of options under this extended model. We show that this extension allows for a better fit to the market data. Finally, we analyse the parameters of this extended model in order to understand intuitively the role of these parameters in the volatility surface. en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher University College Cork en
dc.rights © 2014, Gearóid Ryan. en
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ en
dc.subject Option pricing en
dc.subject Stochastic volatility en
dc.subject Hobson and Rogers model en
dc.title A study of the Hobson and Rogers volatility model en
dc.type Doctoral thesis en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD (Science) en
dc.internal.availability Full text available en
dc.check.info No embargo required en
dc.description.version Accepted Version
dc.contributor.funder Edgeworth Centre for Financial Mathematics, Dublin City University en
dc.description.status Not peer reviewed en
dc.internal.school Mathematics en
dc.check.type No Embargo Required
dc.check.reason No embargo required en
dc.check.opt-out Not applicable en
dc.thesis.opt-out false
dc.check.embargoformat Not applicable en
ucc.workflow.supervisor t.carroll@ucc.ie
dc.internal.conferring Spring Conferring 2015

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© 2014, Gearóid Ryan. Except where otherwise noted, this item's license is described as © 2014, Gearóid Ryan.
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