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Calibration of Local Volatility Models and Proper Orthogonal Decomposition Reduced Order Modeling for Stochastic Volatility Models

Title: Calibration of Local Volatility Models and Proper Orthogonal Decomposition Reduced Order Modeling for Stochastic Volatility Models.
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Name(s): Geng, Jian, author
Navon, Ionel Michael, professor directing dissertation
Case, Bettye Anne, professor co-directing dissertation
Contreras, Rob, university representative
Okten, Giray, committee member
Kercheval, Alec N., committee member
Ewald, Brian, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2013
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: There are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the calibration of stochastic volatility models. In the first part of this thesis (chapters II-III), the local volatility models are introduced first and then calibrated for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both local volatility models with known analytical solutions of European option prices and real market option data. In the second part of this thesis (chapters IV-V), stochastic volatility models, POD reduced order modeling are introduced first respectively. Then POD reduced order modeling is applied to the Heston stochastic volatility model for the pricing of European options. Finally, chapter VI summaries the thesis and points out future research areas.
Identifier: FSU_migr_etd-7388 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2013.
Date of Defense: June 14, 2013.
Keywords: calibration, local volatility surface, POD reduced order modeling, stochastic volatility model, Tikhonov regularization
Bibliography Note: Includes bibliographical references.
Advisory Committee: Ionel Michael Navon, Professor Directing Dissertation; Bettye Anne Case, Professor Co-Directing Dissertation; Rob Contreras, University Representative; Giray Okten, Committee Member; Alec N. Kercheval, Committee Member; Brian Ewald, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-7388
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Host Institution: FSU

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Geng, J. (2013). Calibration of Local Volatility Models and Proper Orthogonal Decomposition Reduced Order Modeling for Stochastic Volatility Models. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-7388