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Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives

Title: Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives.
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Name(s): Liang, Tianyu, 1982-, author
Kercheval, Alec N., professor co-directing dissertation
Wang, Xiaoming, professor co-directing dissertation
Liu, , Guosheng, university representative
Ewald, Brian, committee member
Nichols, Warren D., committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2012
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the mean-reverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closed-form formulas up to first order asymptotic solutions. We also implement multiplicative noise to arithmetic Ornstein-Uhlenbeck process to produce a wider variety of effects. Calibration and Monte Carlo simulation results show that the proposed model outperform Fouque's original stochastic volatility model during some particular window in history. A more efficient numerical scheme, the heterogeneous multi-scale method (HMM), is introduced to simulate the multi-scale differential equations discussed over the chapters.
Identifier: FSU_migr_etd-4990 (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: Spring Semester, 2012.
Date of Defense: February 9, 2012.
Keywords: asymptotic approach, equity derivative, interest rate derivative, Monte Carlo simulation, multi-scale, stochastic volatility
Bibliography Note: Includes bibliographical references.
Advisory Committee: Alec N. Kercheval, Professor Co-Directing Dissertation; Xiaoming Wang, Professor Co-Directing Dissertation; Liu, Guosheng, University Representative; Brian Ewald, Committee Member; Warren D. Nichols, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-4990
Host Institution: FSU

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Liang, T. (2012). Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-4990