Option Pricing Under Rough Heston Model With Jumps

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dc.contributor.advisorQiu, Jinnao
dc.contributor.advisorBadescu, Alexandru
dc.contributor.authorJin, Yazhao
dc.contributor.committeememberLu, Xuewen
dc.contributor.committeememberSwishchuk, Anatoliy
dc.date2022-11
dc.date.accessioned2022-09-27T22:03:40Z
dc.date.available2022-09-27T22:03:40Z
dc.date.issued2022-09
dc.description.abstractThe rough Heston model with jumps is proposed and studied in the thesis which is inspired by some well-known models, including the Heston model, rough Heston model, and Kou's jump model. Our new model considers adding a Poisson jump process to the rough Heston model, which not only keeps the roughness of the volatility process, and also adds an extra noise to improve the model performance. To have better comparisons across models and to understand well how the jumps and roughness improve the model performance, we involve another interesting model called the Heston model with jumps where we used the similar jump process as in Kou's model. The concerned topics are reviewed in the front part of the thesis including option pricing methods, Fourier-inversion techniques, Black-Scholes implied volatilities, and the introduction of related models such as model dynamics and their characteristic functions/moment-generating-functions. In the empirical analysis section, two option pricing methods were compared in the dimension of accuracy and efficiency by the results from Monte Carlo's simulation and their CPU computational time. The calibration based on implied volatilities were processed by four discussed models we mentioned above: the Heston model, rough Heston model, Heston model with jumps, and rough Heston model with jumps. We have the in- and out-of-sample tests to monitor the performances of the models by using the 2014-2019 S&P 500 options, where the former test focuses on the calibrated implied volatilities and the latter conducts a time-series forecast based on the in-sample test results. Significant improvements are shown in the rough Heston model with jumps in both tests which lead us to the conclusion that the combination of the volatility roughness and the add-on Poisson jump process can help the model to reach a better performance.en_US
dc.identifier.citationJin, Y. (2022). Option pricing under rough Heston model with jumps (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.urihttp://hdl.handle.net/1880/115303
dc.identifier.urihttps://dx.doi.org/10.11575/PRISM/40309
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity 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.subjectHeston modelen_US
dc.subjectrough Heston modelen_US
dc.subjectvolatility processen_US
dc.subjectjump-diffusion processen_US
dc.subjectaffine processen_US
dc.subjectaffine Volterra processen_US
dc.subjectPoisson processen_US
dc.subjectimplied volatilityen_US
dc.subjectcalibrationen_US
dc.subjectoption pricingen_US
dc.subjectFourier transformen_US
dc.subjectcharacteristic function/moment-generating-functionen_US
dc.subject.classificationEducation--Financeen_US
dc.subject.classificationMathematicsen_US
dc.titleOption Pricing Under Rough Heston Model With Jumpsen_US
dc.typemaster thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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