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A FULLY DISCRETE APPROACH FOR ESTIMATING LOCAL VOLATILITY IN A
GENERALIZED BLACK-SCHOLES SETTING
by
Oleksandr Lytvak
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2008
Copyright 2008 Oleksandr Lytvak
Object Description
| Title | A fully discrete approach for estimating local volatility in a generalized Black-Scholes setting |
| Author | Lytvak, Oleksandr |
| Author email | lytvak@usc.edu; lytvak@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-06-18 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-07-31 |
| Advisor (committee chair) | Rosen, Gary |
| Advisor (committee member) |
Lototsky, Sergey Westerfield, Mark |
| Abstract | We consider a generalized Black-Scholes model which is used for pricing derivative securities. A fully discrete approximation framework based on the factor-method developed by Krein is presented for the solution of the associated inverse problem. The scheme allows one to estimate a parameter, local volatility, which is extremely important in the theory and practice of financial markets. Volatility is a function of the spatial and temporal variables which appear in the Black-Scholes partial differential equation. Theoretical convergence results are established. A numerical scheme utilizing the advantage of full discretization along with the adjoint method are presented and discussed. The usage of the adjoint method allows for the computation of the gradient of the cost functional precisely in a computationally efficient manner. |
| Keyword | local volatility; inverse problem; Black-Scholes model; factor-method for evolution equations; adjoint method |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1489 |
| Rights | Lytvak, Oleksandr |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Lytvak-2248 |
| Archival file | uscthesesreloadpub_Volume29/etd-Lytvak-2248.pdf |
Description
| Title | Page 1 |
| Full text | A FULLY DISCRETE APPROACH FOR ESTIMATING LOCAL VOLATILITY IN A GENERALIZED BLACK-SCHOLES SETTING by Oleksandr Lytvak A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2008 Copyright 2008 Oleksandr Lytvak |
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